(a)The acceleration of the 1,400-kg boat will be 0.425 m/sec²
(b) If it starts from rest, the distance through which the boat moves in 20.0 s will be 85 m.
(c)Velocity at the end of that time will be 8.5 m/sec.
What is velocity?The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
Given data;
Forwad force acting on the boat,v₁ = 1,800-N
Resistive force acting on the boat,v₂ = 1,200-N
The acceleration of the boat,a
Mass of boat,m = 1,400-kg
Initial velocity of boat,u= 0 m/sec
Distance travelled by boat,S = ?
Time for the boat travels,t = 20.0 s
Final velocity,V = ? m/sec
The net force on the boat;
F = F₁ - F₂
F = 1800 N - 1200 N
F = 600 N
From the defination of force;
F= ma
a = F / m
a = 600 N / 1400 kg
a = 0.425 m/sec²
b)
The distance through which the boat moves is 20.0 s;
[tex]\rm x_f = x_ 0 + v_0 t + \frac{1}{2} at^2 \\\\ x_f = \frac{1}{2}at^2 \\\\ x_f = 0+0 + \frac{1}{2} at^2 \\\\ x_f = \frac{1}{2}\times 0.425 \times (20 )^ 2 \\\\ x_f = 85 \ m[/tex]
c)
The velocity at the end of that time is found as;
[tex]\rm v_f = v_ 0 + at \\\\ v_f =- 0+ at \\\\ v_f = 8.5[/tex] m/sec
Hence the acceleration of the boat, the distance through which the boat moves in 20.0 s, and velocity at the end of that time will be 0.425 m/sec²,85 m, and 8.5 m/sec.
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A 0.145 kg ball moving in the +x direction at 14 m/s is hit by a bat. The ball's final velocity is 20.0 m/s in the -x direction. The bat acts on the ball for a duration of 0.010 s.
Find the average force exerted on the ball by the bat. Include the sign of the force to indicate the direction of the force.
Answer:
Approximately [tex](-4.9\times 10^{2}\; {\rm N})[/tex] (rounded to two significant figures.)
Explanation:
The impulse [tex]\mathbf{J}[/tex] on an object is equal to the change in the momentum [tex]\mathbf{p}[/tex] of this object. Dividing impulse by duration [tex]\Delta t[/tex] of the contact would give the average external force that was exerted on this object.
If an object of mass [tex]m[/tex] is moving at a velocity of [tex]\mathbf{v}[/tex], the momentum of that object would be [tex]\mathbf{p} = m\, \mathbf{v}[/tex].
Let [tex]m[/tex] denote the speed of this ball. Let [tex]\mathbf{v}_{0}[/tex] denote the velocity of this ball before the contact, and let [tex]\mathbf{v}_{1}[/tex] denote the velocity of the ball after the contact.
Momentum [tex]\mathbf{p}_{0}[/tex] of this ball before the contact: [tex]\mathbf{p}_{0} = m\, \mathbf{v}_{0}[/tex].
Momentum [tex]\mathbf{p}_{1}[/tex] of this ball after the contact: [tex]\mathbf{p}_{1} = m\, \mathbf{v}_{1}[/tex].
Impulse, which is equal to the change in momentum:
[tex]\mathbf{J} = \mathbf{p}_{1} - \mathbf{p}_{0} = m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}[/tex].
Since the velocity of the ball after the contact is in the [tex](-x)[/tex] direction, [tex]\mathbf{v}_{1} = -20.0\; {\rm m\cdot s^{-1}}[/tex]. The average external force on this ball would be:
[tex]\begin{aligned} \mathbf{F} &= \frac{\mathbf{J}}{\Delta t} \\ &= \frac{m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}}{\Delta t} \\ &= \frac{m\, (\mathbf{v}_{1} - \mathbf{v}_{0})}{\Delta t} \\ &= \frac{0.145\; {\rm kg} \times ((-20.0\; {\rm m\cdot s^{-1}}) - 14\; {\rm m\cdot s^{-1}})}{0.010\; {\rm s}} \\ &\approx -4.9 \times 10^{2}\; {\rm N}\end{aligned}[/tex].
(Rounded to two significant figures.)
M, a solid cylinder (M=2.15 kg, R=0.111 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.730 kg mass, i.e., F = 7.161 N.
1. Calculate the angular acceleration of the cylinder.
2. If instead of the force F an actual mass m = 0.730 kg is hung from the string, find the angular acceleration of the cylinder.
3. How far does m travel downward between 0.390 s and 0.590 s after the motion begins?
4. The cylinder is changed to one with the same mass and radius, but a different moment of inertia. Starting from rest, the mass now moves a distance 0.450 m in a time of 0.490 s. Find I[tex]_{cm}[/tex] of the new cylinder.
Hi there!
1.
Let's use the rotational equivalent of Newton's Second Law.
[tex]\Sigma \tau = I\alpha[/tex]
τ = Torque (Nm)
I = Moment of Inertia (1/2mR² for solid cylinder)
α = Angular acceleration (rad/sec²)
The torque is equivalent to:
[tex]\tau = r \times F[/tex]
r = distance from lever arm to pivot point, aka the radius for this cylinder (0.111 m)
F = applied force (7.161 N)
We are already given various values, so let's create a working equation and solve.
[tex]rF = I\alpha \\\\\alpha = \frac{rF}{I}[/tex]
[tex]\alpha = \frac{(0.111)(7.161)}{\frac{1}{2}(2.15)(0.111^2)} = \boxed{60.013 \frac{rad}{sec^2}}[/tex]
2.
So, let's begin by doing a summation of forces acting on the block.
We have its force of gravity downward(+), and the tension from the string upward. (-), assigning signs based on the path of the falling block.
[tex]\Sigma F = F_g - T\\\\\Sigma F = m_b g - T\\\\m_b a = m_b g - T[/tex]
Solving for 'T':
[tex]T = m_b g - m_b a[/tex]
Let's now do a summation of torques on the cylinder. We only have the torque caused by the tension in the string connected to the block.
[tex]\Sigma \tau = rT\\\\I\alpha = r(T = m_b g - m_b a)[/tex]
Using the relationship between angular and translational acceleration:
[tex]a = \alpha r\\\\alpha = \frac{a}{r}[/tex]
And the equation for the moment of inertia:
[tex]I = \frac{1}{2}Mr^2[/tex]
Simplify the expression.
[tex]\frac{1}{2}Mr^2(\frac{a}{r}) = r( m_b g - m_b a)\\\\\frac{1}{2}Ma = ( m_b g - m_b a)[/tex]
Solve for 'a':
[tex]\frac{1}{2}ma + m_b a= m_b g \\\\a = \frac{m_b g}{\frac{1}{2}M + m_b} = \frac{0.730(9.81)}{\frac{1}{2}(2.15) + 0.730} = \boxed{3.97 \frac{m}{s^2}}[/tex]
3.
This is just a case of kinematics since we have a constant acceleration. To solve for this instance, however, let's use calculus.
We know that:
[tex]a(t) = 3.97[/tex]
v(t) is the integral. There is no initial velocity (block starts from rest), so:
[tex]v(t) = 3.97t + C\\C = 0 m/s \\\\v(t) = 3.97t[/tex]
Now, we can take the integral of the velocity/time equation to find the displacement between the interval.
[tex]\int\limits^{0.590}_{0.390} {3.97t} \, dt = \boxed{0.389 m}[/tex]
4.
So, let's now find the translational acceleration produced by the new cylinder. Use the kinematic equation:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]
Since the block starts from rest, we can do some simplifying and rearranging:
[tex]2\Delta x = at^2\\\\a = \frac{2\Delta x}{t^2} = \frac{2(0.450)}{0.490^2} = 3.748 \frac{m}{s}^2[/tex]
So, let's go back to our summation of torques equation. This time, however, we cannot simplify 'I'.
[tex]I(\frac{a}{r}) = r( m_b g - m_b a)[/tex]
Solving for 'I':
[tex]I = \frac{r^2( m_b g - m_b a)}{a} = \frac{(0.111^2)(7.161 - .730(3.748))}{3.748}\\\\ = \boxed{0.0145 kgm^2}[/tex]
An emf source with a magnitude of E = 120.0 V, a resistor with a resistance of R = 89.0 Ω, and a capacitor with a capacitance of C = 6.00 μF are connected in series. A) As the capacitor charges, when the current in the resistor is 0.950 A , what is the magnitude of the charge on each plate of the capacitor?
For an emf source with a magnitude of E = 120.0 V, is mathematically given as
Q=136.63uC
What is the magnitude of the charge on each plate of the capacitor?Parameters
E = 120.0 VR = 89.0 ΩC = 6.00 μFGenerally, the equation for voltage on the resistor is mathematically given as
Vr=IR
Therefore
Vr=71*0.95
Vr=67.45V
voltage on capacitor
Vc=120-67.45
Vc=52.55V
In conclusion,
Q=CVc
Therefore
Q=52.55*2.60
Q=136.63uC
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Two point charges q1 and q2 are located at (2.0, 0.0) cm and (8.0, 0.0) cm,
respectively. A positive point charge q3 is placed somewhere so that the net
electrostatic force acting on it due to q1 and q2 is zero. Find the position of q3 if
q1 = 2.0 μC and q2 = -8.0 μC. Sketch a figure that shows the position of all
three point charges and the forces acting on q3.
The Sketch of the figure will bear the parameters of the charge that lies at (4,0,0)
What is co-ordinate of the charge?Generally, the equation for is mathematically given as
1)
Since both of the other points, "q1"<"q2," are on the x-axis, the third one must also be on the x-axis, and it must be close to the charge of lesser magnitude. off q1 by x cm
Now, forces on q3 due to q1
[tex]\vec{F}_{1}=\frac{k q_{1} q_{3}}{x^{2}} \hat{x}[/tex]
Force on q3 due to q2
[tex]\vec{F}_{2}=\frac{k q_{2} q_{3}}{(6+x)^{2}}(-\hat{x})[/tex]
[tex]\quad \vec{F}_{1}+\vec{G}_{2}=0$[/tex]
[tex]&\frac{k q_{1} q_{3}}{x^{2}}-\frac{k q_{2} q_{3}}{(x+6)^{2}}=0 \\&\frac{2}{x^{2}}=\frac{8}{(x+6)^{2}} \Rightarrow \frac{x+6}{x}=\sqrt{\frac{8}{2}}=2 \\&x+6=2 x \Rightarrow x=6 \mathrm{~cm}[/tex]
In conclusion, the charge lies at (4,0,0)
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two object of masses 80kg and 50kg are separated by a distance 0.2m. If the gravitational constant is 6.6 × 10^-11 Nm^2 kg^-2, calculate the gravitational attraction between them.
The gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.
What is Newton's law of gravitation?Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Given data
Mass of object 1,m = 80 kg
Mass of object 2,M = 50 kg
Gravitational constant,G = 6.6 × 10⁻¹¹ kg⁻² m²
Distance of seperation,R = 0.2 m
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
[tex]\rm F = G\frac{mM}{R^ 2} \\\\ F = 6.6 \times 10^{-11 }\times \frac{80 \times 50 }{(0.2)^2} \\\\F = 6.6 \times 10^{-6 } \ N[/tex]
Hence the gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.
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A water wave has a frequency of 6 Hz and a wavelength of 3 m. (a) What is the period of these waves? (b) What is the wave velocity?
The period or time duration of these waves is 0.16 sec. While the wave velocity is 18m/sec.
What is Wavelength?Wavelength may be defined as the space between equivalent points in the contiguous cycles of a waveform signal propagated in the area or along a wire.
The time duration of these waves is calculated by the given formula:
T = [tex]\frac{1}{F}[/tex] = [tex]\frac{1}{6}[/tex] = 0.16 seconds.
The velocity is calculated by the given formula:
V= Wavelength × Frequency = 6Hz × 3m = 18m/sec.
Therefore, it is well described above.
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A tennis player tosses a tennis ball straight up and then catches it after 2.07 s at the same height as the point of release.
(a) What is the acceleration of the ball while it is in flight?
magnitude
m/s2
direction
---Select---
(b) What is the velocity of the ball when it reaches its maximum height?
magnitude
m/s
direction
---Select---
(c) Find the initial velocity of the ball.
m/s upward
(d) Find the maximum height it reaches.
m
(a)The acceleration of the ball, while it is in flight, will be 9.81 m/s².
(b) The velocity of the ball when it reaches its maximum height will be 0 m/sec.
(c) The initial velocity of the ball is 20.30 m/s upward.
(d) The maximum height it reaches will be 21.00 m
What is velocity?The change of displacement with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is;
u is the initial velocity of fall = ? m/sec
h is the distance of fall = ? m
g is the acceleration of free fall = 9.81 m/sec²
a.
The acceleration of the ball, while it is in flight, is equal to the acceleration due to gravity,g=9.81 m/s².
b.
The ball's velocity will be zero when it has reached its highest point.
c.
The initial velocity of the ball is;
v=u-gt
0=u-gt
u=gt
u=9.81 m/s² × 2.07 sec
u=20.30 m/s
d.
The maximum height it reaches is found by the formula as;
[tex]\rm u^2 = - 2gh \\\\ (20.30)^2 = -2 \times (-9.8) \times h \\\\ 412.09 = 19.6 \times h\\\\ h = 412.09/19.6\\\\ h = 21.00 m[/tex]
Hence the acceleration of the ball,s the velocity of the ball when it reaches its maximum height, the initial velocity of the ball, and the maximum height it reaches will be 9.81 m/s²,0 m/sec,20.30 m/s, and 21.00 m respectively.
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A ball starts rolling down a ramp. What is the value of the change in its kinetic energy, ΔEk?
Positive
Zero
Negative
For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive
Meaning of Kinetic energyKinetic energy can be defined as the ability assumed by an object in motion.
Kinetic energy is also said to be a form of mechanical energy that is possessed by an object to be in motion.
In conclusion, For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive
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A crane lifts up two boxes. A picture of a crane with a cable hanging down labeled Rope 1, which is attached to a box labeled A. Box A is attached to a cable labeled Rope 2, which is attached to a box labeled B. Which free body diagram shows the forces acting on block A? A free body diagram with two force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline. A free body diagram with three force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline, and the third pointing downward labeled F Subscript g B. A free body diagram with three force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline, and the third pointing downward labeled F Subscript T 2. A free body diagram with three force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline, and the third pointing upward labeled F Subscript T 2.
The free body diagram showing the forces acting on block A is diagram 3; option C.
What are free body diagrams?Free body diagrams are simple diagrams which are used to illustrate the magnitude and direction of the forces acting on the body.
The diagram of the crane and boxes as well as the free body diagrams are shown in the attached image.
Three forces are acting on A as follows:
The force of gravity acting downward, represented by [tex]F_{gA}[/tex]The tension in the rope 1, pulling block A upwards, represented by [tex]F_{T1}[/tex]The tension in the rope 2, due to the weight of block B, pulling block A downwards, represented by [tex]F_{T2}[/tex]Therefore, diagram 3 is correct.
In conclusion, free body diagram shows the forces acting on a body as well as their direction of action.
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Answer:
I think C is the correct answer
Explanation:
The temperature of the filament is 2500 K when the bulb is switched on. The diameter of the filament is 0.1 mm and it is made of metal of emissivity 0.35. If the emissive power is 40 W find the length of the filament.
The length of the filament is 0.2 m.
To find the answer, we need to know about the Stefan - Boltzmann law.
What's Stefan - Boltzmann law?It states that the intensity of power radiated from a body is propertional to the fourth power of temperature of the object.Mathematically, I= e×σ×T⁴I= intensity, e= emissivity, σ= a constant with value 5.67×10^(-8) W/(m²K⁴), T= temperatureAs intensity= power/area, so power= area ×e×σ×T⁴What's the length of the filament having diameter 0.1 mm, temperature 2500K, emissivity 0.35 and radiating power of 40W?Here, e= 0.35, T= 2500K, power= 40WIf L= length of the filament, its area = (2πd/2)L= πdLSo, power= π×d×L ×e×σ×T⁴L= power/(π×d×e×σ×T⁴)
= 40/(π×0.0001×0.35×5.67×10^(-8)×2500⁴)
= 0.2m
Thus, we can conclude that the length of the filament is 0.2 m.
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The electric field in a region points to the northeast. What is the direction of the acceleration of an electron
placed in this region? Consider only the electric force.
northeast
None of the other answers are correct.
northwest
southwest
southeast
Answer:
Southwest. The electric force on this electron would point southwest (opposite to the direction of the electric field.)
Explanation:
Consider a position in an electric field. A positive point charge placed at that position would experience an electric force from this field. By definition, the direction of this field at that position would be the same as the direction of electric force that the field exerts on the positive point charge placed at that position.
It is given that the electric field in this question points to the northeast in this region. Thus, a positive point charge placed in this region would experience an electric force in the same direction- to the northeast.
Electrons are negatively charged. The direction of electric force on an electron would be opposite to that on a positive point charge placed at the same position. The electric force on a positive point charge in this region points to the northeast (same as the direction of the electric field). The opposite of northeast is southwest. Hence, the electric force on an electron at this position would point to the southwest.
Find the kenetic energy of a car of mass 700kg racing with a velocity of 10m/s
Answer:
35000 KJ
Explanation:
The equation for the kinetic energy is given by the formula :
[tex]E_{k} = \frac{1}{2} mv^{2}[/tex]
[tex]E_{k} = \frac{1}{2} (700)(10)^{2}[/tex]
[tex]E_{k} = \frac{1}{2} (700)(100)[/tex]
[tex]E_{k} = (350)(100)[/tex] OR [tex]E_{k} = \frac{1}{2} (70000)[/tex]
[tex]E_{k} = 35000[/tex]
Units will be kilojoules since the units of mass was kilograms .
Our final answer is 35000 KJ
Hope this helped and have a good day
Example No. 10
In a worst-case design scenario, a 2000 kg elevator with broken cables is
falling at 8.0 m/s when it first contact a cushioning spring at the bottom
of the shaft. The spring is supposed to stop the elevator, compressing 3.0
m as it does so. Determine what the force constant of the spring should
be.
The force constant of the spring is determined as 14,222.2 N/m.
Force constant of the springApply the principle of conservation of energy,
K.E = U
where;
K.E kinetic energy of the elevatorU is elastic potential energy of the spring¹/₂mv² = ¹/₂kx²
mv² = kx²
k = mv²/x²
Where;
m is mass of the elevatorv is speedx is compression of the springk = (2000 x 8²)/(3²)
k = 14,222.2 N/m
Thus, the force constant of the spring is determined as 14,222.2 N/m.
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A voltmeter of 600ohms resistance reads 200v when connected across a battery of 3ohms internal resistance. Calculate the emf of the battery
The emf of the battery will be 2.955 V. The rate of change of magnetic flux linked with the coil is responsible for generating emf.
What is induced voltage?Electromagnetic induction is what causes the induced voltage. Electromagnetic induction generates emf (induced voltage) by subjecting a conductor to a magnetic field.
Given data;
Voltage,v = 200 v
Resistance, r=600 ohms
Internal resistance,R = 3 ohms
The EMF of the battery is found as follows;
E = {vR}/{R+r}
E = 200×3/(3 + 200)
E = 2.955 V
Hence, the emf of the battery will be 2.955 V.
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Which includes the definition of both Behaviorism and Psychoanalysis approaches?
Behaviorism approach centers on giving absolute prominence to the outside characters of individuals
What is Psychoanalysis approaches?Psychoanalysis approach centers on fact the fact that the unconscious has the potential to drive our behavior
Interestingly, the behaviorists and psychoanalysts share some common norms and values in such away that
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calculate the pressure of water in a will if the deep of the water is 10 m
Answer:
98,000 pa
Explanation:
The formula for water pressure is as follows:
[tex]pressure = pgh[/tex]
Where p is the density of water (in kg/m3), g is the gravitational field strength, and h is the height of the water.
The density of water is 1000kg/m3, the gravitational field strength is 9.8, and the height is 10. Substituting in these values:
[tex]pressure = 1000 \times 9.8 \times 10[/tex]
[tex]pressure = 98000[/tex]
which of these are lost when the body repairs?
oxygen and calcium
calcium and sodium
sodium and potassium
potassium and oxygen
c. Sodium and potassium
What is called perspiration?Perspiration, water given off by the intact skin, either as vapor by simple evaporation from the epidermis or as sweat, a form of cooling in which liquid actively secreted from sweat glands evaporates from the body surface.
When our body is sweating sodium and potassium is lost from the body along with water.
In order to maintain the integrity of the cells in the body ,Sodium and potassium are very important.
Sweat is also known as perspiration.
So,
By maintaining the proper cell functioning and cell vitality optimum level of sodium and potassium should be maintained in the body.
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Two people are dragging a canoe on a beach using light ropes. Person 1 applies a
force of 60.0N [Forward] and person 2 applies a force of 90.0N [Forward]. The
friction exerted by the beach on the canoe is 85.0N. Determine the net force of the
canoe.
a) 50.0 N [forward]
Ob) 6.50 N [backward]
c) 6.50 N [forward]
d) 65.0 N [forward]
The net force on the canoe is obtained as 65.0 N [forward]
What is the frictional force?The frictional force is the force that opposes motion. We know that the net force is the actual force that moves the canoe in a given direction.
Hence, the total force acting in the forward direction = 60.0N + 90.0N = 150 N and the total backwards force = 85.0N
Net force = 150 N - 85.0N = 65.0 N [forward]
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A section of a high speed test track is circular with a radius of curvature R = 1860 m.
At what angle of θ should the track be inclined so that a car traveling at 61.0 m/s (136 mph) would keep moving in a circle if there is oil on that section of the track, i.e., it would not slip sideways even with zero friction on that section. (Hint: The car's vertical acceleration is zero)
From the calculation, the banking angle is obtained as 11.5°.
What is the banking angle?The banking angle refers to the angle at which the vehicle must be inclined so that it does not skid off the road.
Now we have;
θ = ?
v = 61.0 m/s
r = 1860 m
g = 9.8 m/s^2
θ = tan-1(61^2/ 1860 * 9.8)
θ = tan-1(3721)/18228
θ = 11.5°
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Abdou was explaining to a classmate that graphite is a good lubricant
because it is bonded in layers that easily slip over each other. Which image
shows this quality?
The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other.
Why is graphite a solid lubricant?We know that graphite is composed of layers. These hexagonal layers are held together by weak Van Der Walls forces and as such are able to slide over each other. The carbon atom in each layer are held together by strong covalent bonds.
The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other and as such make the graphite fluid.
Thus, the image that shows these layers of graphite is attached to this an answer
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Answer:it’s B
Explanation:
1. Is it reasonable to expect that anyone would be able to make good sense of a filing system such as this new one? Why or why not?
It reasonable to expect that anyone would be able to make good sense of a filing system as it reduces the overall storage space occupied by the records.
What is Filing?This is the process of keeping document safely and being able to easily retrieve them.
The new filing system is based on their volume which is why the space is reduced thereby reducing the ambiguity.
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A long rope is fixed at one end, and the free end is made to oscillate in one plane at right angles to the rope with frequency 5Hz. The successive crests are 60cm apart. What is the speed of the waves? For what frequency would the wavelength be 0.4m?
Answer:
See below
Explanation:
speed = freq * wavelength
= 5 Hz * .6 m = 3 m/s
speed = freq * wavelength
3 = freq * .4 m freq = 7.5 hz
1. The speed of the waves is 3 m/s. 2. for a wavelength of 0.4 m, the frequency would be 7.5 Hz.
To find the speed of the waves, we can use the equation:
[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]
Given that the frequency is 5 Hz and the distance between successive crests (wavelength) is 60 cm, we need to convert the wavelength to meters:
[tex]\[ \text{Wavelength} = 60 \, \text{cm} = 0.6 \, \text{m} \][/tex]
Plugging in the values, we have:
[tex]\[ \text{Speed} = 5 \, \text{Hz} \times 0.6 \, \text{m} = 3 \, \text{m/s} \][/tex]
Therefore, the speed of the waves is 3 m/s.
Now, to find the frequency at which the wavelength is 0.4 m, we rearrange the equation:
[tex]\[ \text{Frequency} = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]
Substituting the given values:
[tex]\[ \text{Frequency} = \frac{3 \, \text{m/s}}{0.4 \, \text{m}} = 7.5 \, \text{Hz} \][/tex]
Thus, for a wavelength of 0.4 m, the frequency would be 7.5 Hz.
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A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k1 and k2 whose opposite ends are fixed to walls. What is angular frequency of the oscillation if k1= 9.5 N/m and k2= 5 N/m?
The angular frequency of the oscillation is determined as 2.7 rad/s.
Angular frequency of the block
ω = √k/m
With respect to spring constant k1 and k2
k1 + k2 = 9.5 N/m + 5 N/m = 14.5 N/m
ω = √14.5/2 = 2.7 rad/s
Thus, the angular frequency of the oscillation is determined as 2.7 rad/s.
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the density of gas is 1.775kg/m^3 at 27 degree celcius and pressure of 10^-5n/m^2. if the specific heat capacity at constant pressure is 846 jkg^-1k^-1 calculate the ratio of specific heat capacity at constant pressure to tht constant volume
Answer:
76.52
Explanation:
the density of gas is 1.775kg/m^3 at 27 degree celcius and pressure of 10^-5n/m^2. if the specific heat capacity at constant pressure is 846 jkg^-1k^-1, the ratio of specific heat capacity at constant pressure to tht constant volume is 76.52
what is density?Density is the mass of a unit volume of a material substance. The formula for density is represented by d = M/V, where d is density, M is mass, and V is volume.
It is commonly represented in units of grams per cubic centimeter. Density can also be expressed as kilograms per cubic meter .
Density can used to define how different materials interact when mixed together. For example Wood floats in water because it has a lower density, while an anchor sinks because the metal has a higher density.
density can be applied in pipe design, shipbuilding, helium balloons, weight distribution in the aeroplane, and the fact that ice floats on water.
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A big rock falls from a height towards water below, and hits water at a speed of 12 m/s. Rock was at a height of 15 m before falling and weighs 65 kg.
a) What was the average force of air resistance (e.g., friction) acting on the rock?
b) What is the force of friction underwater if the rock reaches a depth of 2.5 m before stopping and there is a buoyant force of 650 N [upward] acting on the rock once underwater.
The frictional force of air resistance is; 949N while the force of friction underwater is; 1859N.
What is the Frictional force of air resistance?The frictional force on the action rock can be evaluated as follows;
F - W = ma
However, the acceleration of fall a can be evaluated as follows;
a = (12² -0²)/2× 15
a = 144/30 = 4.8m/s².
a) Hence, the air resistance, frictional force, F = (65×9.8) + (65 ×4.8)
F = 949N.
b) When reaches a depth of 2.5m, it follows that the acceleration is;
a = (0²-12²)/(2×2.5)
a = 144/5 = 28.8m/s².
On this note, the force balance is;
F + 650 = 65(9.8 + 28.8)
F = 2509 - 650
F = 1859N.
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Many television sets show 25 images, called 'frames, each second. What is the time interval between one
frame and the next?
Answer:
Given,
Frame rate = 25 frames per second
To find,
Time interval between one frame and the next.
Solution,
We can simply solve this numerical problem by using the following process.
Now,
Number of frames = 25
Total time taken to display the given number of frames (ie. 25 frames) = 1 second
To calculate the time interval between one frame and next, we need to divide the time taken to display total number of frames by total number of frames.
So,
Time interval between one frame and next :
= Time taken to display total number of frames / Total frames
= 1/25
= 0.04 second
Hence, time interval between one frame and next is 0.04 second.
Assuming barber wants to setup a saloon in a measuring length of 3m by 3m. He has a simple wooden chairs,3 large mirror and one bulb. Using the knowledge of shadows and reflection, advice the barber on how to arrange a good saloon using the only item he has. Without adding more source of light, how can he enhance the lighting system in his saloon?
The best way to arrange the salon to best use what he has is:
Place the bulb in the middle of the wallDirectly face the chair and mirror in front of the bulb for proper lighting and reflectionPlace the chairs side by side of each otherEach mirror should be facing each chaiWhat is Reflection?This refers to the change in direction of a wavefront between two different media so that the wavefront returns to its originating medium.
Hence, we can see that from our knowledge of shadows and reflection, we can note that mirrors reflect and light helps to bring detail in a dark area and the chairs should be facing the mirrors directly so the customer can see his hair and how it is being cut by the barber.
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A roller coaster's velocity at the bottom of a hill is 35.0 m/s, 5.00 seconds later it reaches the top of the hill with a velocity of 10.0
m/s. What was the deceleration of the coaster?
O 5.00 m/s/s
O 7.00 m/s/s
O 2.00 m/s/s
O 25.0 m/s/s
Answer:
5 m /s^2
Explanation:
Change in velocity = 35 - 10 = 25 m/s
change in time = 5 s
decelleration = 25/5 = 5 m/s^2
What is the mass of mars
Answer:
6.39 × 10^23 kg
.........
6.A truck is carrying a steel beam of length 13.0 m on a freeway. An accident causes the beam to be dumped off the truck and slide horizontally along the ground at a speed of 30.0 m/s. The velocity of the center of mass of the beam is northward while the length of the beam maintains an east–west orientation. The vertical component of the Earth's magnetic field at this location has a magnitude of 30.0 T. What is the magnitude of the induced emf between the ends of the beam?
The magnitude is 13.12 mV.
The steps are attached below.
How do you find the magnitude of an induced emf?The standard SI unit of the magnetic field is the tesla (T). As an end result, we can use these equations and the equation for an induced emf due to changes in magnetic flux, ϵ=−NΔϕΔt ϵ = − N Δ ϕ Δ t, to calculate the importance of a precipitated emf in a solenoid.
The magnitude of the precipitated contemporary depends on the rate of trade of magnetic flux or the fee of reducing the magnetic area strains.
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