Answers
Split up the forces into components acting parallel to and perpendicular to the slope. See the attached picture for the reference axes.
The box stays on the surface of the plane, so that the net force acting perpendicular to it is 0, and the only acceleration is applied in the parallel direction.
Let m be the mass of the box, θ the angle the plane makes with the ground, and a the acceleration of the box. By Newton's second law, we have
• net parallel force
∑ Force (//) = W (//) - F = m a
(that is, the net force in the parallel direction is the sum of the parallel component of the weight W and the friction F which acts in the negative direction)
• net perpendicular force
∑ Force (⟂) = W (⟂) + N = 0
Notice that
W (//) = W sin(θ) … … … which is positive since it points down the plane
W (⟂) = -W cos(θ) … … … which is negative since it points opposite the normal force N
So the equations become
W sin(θ) - F = m a
-W cos(θ) + N = 0
Solving for a gives
a = (W sin(θ) - F ) / m
which is good enough if you know the magnitude of the friction force.
If you don't, you can write F in terms of the coefficient of kinetic friction between the box and plane, µ, as
F = µ N
so that
a = (W sin(θ) - µ N ) / m
and the normal force itself has a magnitude of
N = W cos(θ)
so that
a = (W sin(θ) - µ W cos(θ) ) / m
The weight W has magnitude m g, where g is the magnitude of the acceleration due to gravity, so
a = (m g sin(θ) - µ m g cos(θ) ) / m
a = g (sin(θ) - µ cos(θ))
Related Questions
It takes a truck 3.56 seconds to slow down from 112 km/h to 87.4 km/h. What is its average acceleration?
Answers
Answer:
1.92 m/s2
Explanation:
A student throws a baseball upwards at an angle of 60 degrees to the horizontal. The initial
horizontal and vertical components are 12.5 m/s and 21.7 m/s, respectively.
60 degrees
Refer to the above information and diagram. What position will have the smallest magnitude
of vertical velocity?
Answers
Answer:
The initial horizontal and vertical components are 12.5 m/s and 21.7 m/s, respectively?
Explanation:
I am unable to understand from question no 3 and I have assignment due :( in 2 days need to do till 9
Answers
Answer:
Oh well have your parents do something bout that. They are there to help you. Or guardian they all shall help you that is what they are there for. They are they to take care of you, answer you questions, and last but not least, they are there to also raise you. Ask you mom, dad, guardian, and maybe even you teacher to post pone the date. Teachers are to help you. Your guardian is to watch you make sure your safe while your parents are away (bascially like raising you). And parents to raise you, make sure you safe, and many other things like to make sure you are fed.
Explanation:
I hope they all have some type of help for you.
[2.21] Please help me find a) and b)
Answers
Answer:
A. 28.42 m/s
B. 41.21 m.
Explanation:
A. Determination of the initial velocity of the ball:
Time (t) to reach the maximum height = 2.9 s
Final velocity (v) = 0 (at maximum height)
Acceleration due to gravity (g) = –9.8 m/s² (since the ball is going against gravity)
Initial velocity (u) =?
Thus, we can obtain the initial velocity of the ball as follow:
v = u + gt
0 = u + (–9.8 × 2.9)
0 = u – 28.42
Collect like terms
u = 0 + 28.42
u = 28.42 m/s
Therefore, the initial velocity of the ball is 28.42 m/s.
B. Determination of the maximum height reached.
Final velocity (v) = 0 (at maximum height)
Acceleration due to gravity (g) = –9.8 m/s² (since the ball is going against gravity)
Initial velocity (u) = 28.42 m/s.
Maximum height (h) =?
Thus, we can obtain the maximum height reached by the ball as follow:
v² = u² + 2gh
0² = 28.42² + (2 × –9.8 × h)
0 = 807.6964 + (–19.6h)
0 = 807.6964 – 19.6h
Collect like terms
0 – 807.6964 = – 19.6h
– 807.6964 = – 19.6h
Divide both side by – 19.6
h = –807.6964 / –19.6
h = 41.21 m
Therefore, the maximum height reached by the ball is 41.21 m
A 30 N force toward the west is applied to an object. The object moves 50 m east during the time the force is applied. What is the change in kinetic energy of the object?
a) 1.0 J
b) 750 J
c) 1.7 J
d) -1500 J
Answers
Answer:
D.-1500Joules
Explanation:
The change in kinetic energy of the object s equivalent to the workdone by the body in the west direction (negative x direction)
Workdone = Force * Distance
Given
Force = 30N
Distance moved by the object = 30m
Required
Kinetic energy
Kinetic energy = 30 * 50
Kinetic energy = 1500Joules
Since the body moves in the negative direction, hence the kinetic energy will be -1500Joules
Sally and Sam are in a spaceship that comes to within 18,000 km of the asteroid Ceres. Determine the force Sally experiences due to the presence of the asteroid. The mass of the asteroid is 8.7 X 10^20 kg and the mass of Sally is 77 kg. For calculation purposes assume the two objects to be point masses.
Answers
Answer:
F = 0.014 N
Explanation:
Assuming that both masses are point masses, the force that Sally experiences due to the mass of Ceres, is given by the Newton's Universal Law of Gravitation, as follows:[tex]F_{SC} =G *\frac{m_{S}*m_{C} }{r_{SC} ^{2} } (1)[/tex]
where G= Universal Constant of Gravitation = 6.67*10⁻¹¹ N*m2/kg2
mS = mass of Sally = 77 kg.
mC = mass of Ceres = 8.7*10²⁰ kg
rSC = distance between Sally and Ceres = 18,000 km
Replacing by the values, we get:[tex]F_{SC} =6.67e-11 N*m2/kg2 *\frac{77kg*8.7e20kg}{(18,000km)^{2}} = 0.014 N (2)[/tex]
A container contains a number of marbles each having a mass 80 mg. If the total mass of the marbles in the container is 2 kg. find the numbers in the container
Answers
Answer:
There are 25,000 marbles in the container
Explanation:
There is a certain number of marbles in a container.
We know each marble has a mass of 80 mg and we also know the total mass of the marbles in the container is 2 Kg.
Since the data is given in different units of mass, we convert them into one unit in common.
Let's convert 2 Kg to milligrams. There are 1,000 grams in a kilogram, and there are 1,000 milligrams in a gram, thus there are one million milligrams in one kilogram, that is:
1 Kg = 1,000,000 mg
And 2 Kg = 2,000,000 mg
The number of marbles can be found by dividing the total mass by the individual mass:
No. of marbles = 2,000,000 / 80 = 25,000
There are 25,000 marbles in the container
An opera singer who is a baritone, lowers his pitch and raises his voice for a song. Which best describes how the resulting sound wave has changed? The sound wave will have:
a lower amplitude and higher wavelength
a lower amplitude and higher frequency.
a higher amplitude and lower frequency.
a higher amplitude and faster speed
Answers
Answer: 3.
Explanation:
The correct answer is a higher amplitude and lower frequency. Since an opera singer is lowering his pitch it means that he is creating higher amplitude and because he is raising his voice for a song with that higher amplitude he is creating lower frequency.
What is the velocity of an object after falling for 15 seconds, neglecting air resistance? (g=9.81)
O 77.499
O 0.64m/s^2
O 15.53 m/s to the left.
147.15 m/s downward.
Answers
Answer:
(ans147.15m/s downward)
Explanation:
initial velocity (u)=0m/s
final velocity (v)=?
v=u+gt. ( t)time taken=15seconds
?=0+(9.81)×15
?=147.15m/s
hope this helped
A car with a mass of 500 kg, gets off road and goes straight into a cliff of 30 m with an
initial velocity of 50 m/s. What is the car velocity when it hits the ground?
I
Answers
Answer:
The velocity of the car when it hits the ground is approximately 55.574 meters per second.
Explanation:
According to this expression, the car goes straight into the cliff and goes down due to gravity, whose situation is described by the Principle of Energy Conservation and supposing that all non-conservative forces are negligible:
[tex]U_{g,1}+K_{1} = U_{g,2}+K_{2}[/tex] (1)
Where:
[tex]U_{g,1}[/tex], [tex]U_{g,2}[/tex] - Gravitational potential energies of the car at the top and the bottom, measured in joules.
[tex]K_{1}[/tex], [tex]K_{2}[/tex] - Translational kinetic energies of the car at the top and the bottom, measured in joules.
By definitions of gravitational potential and translational kinetic energies, we expand and simplify the equation above:
[tex]\frac{1}{2}\cdot m\cdot v_{2}^{2} = \frac{1}{2}\cdot m \cdot v_{1}^{2}+m\cdot g \cdot (z_{1}-z_{2})[/tex] (2)
[tex]v_{2}^{2} = v_{1}^{2}+2\cdot g\cdot (z_{1}-z_{2})[/tex]
[tex]v_{2} = \sqrt{v_{1}^{2}+2\cdot g\cdot (z_{1}-z_{2})}[/tex]
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]v_{1}[/tex], [tex]v_{2}[/tex] - Velocity of the car at the top and the bottom, measured in meters per second.
[tex]g[/tex] - Gravitaitional acceleration, measured in meters per square second.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Height of the car at the top and at the bottom, measured in meters.
If we know that [tex]v_{1} = 50\,\frac{m}{s}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]z_{1} = 30\,m[/tex] and [tex]z_{2} = 0\,m[/tex], then the velocity of the car when it hits the ground is:
[tex]v_{2} = \sqrt{\left(50\,\frac{m}{s} \right)^{2}+2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (30\,m-0\,m)}[/tex]
[tex]v_{2}\approx 55.574\,\frac{m}{s}[/tex]
The velocity of the car when it hits the ground is approximately 55.574 meters per second.
A vehicle of mass 100kg has a kinetic energy of 5000 J at an instant. The velocity at that instant is
Answers
Answer:
23.51 m/s
Explanation:
Parameters given:
Kinetic energy, K = 295 J
Momentum, p = 25.1 kgm/s
a) The kinetic energy of a body is given as:
where m = mass of the body and v = speed of the body
Answer:
[tex]\bf\pink{10\:m/s}[/tex]Explanation:
Given :-[tex]\sf\red{Mass \ of \ vehicle \ (m) = 100 \ kg}[/tex][tex]\sf\orange{Kinetic \ energy \ (K.E.) = 5000 \ J}[/tex]To Find :-[tex]\sf\green{Velocity\: of\: the \:vehicle \:at \:the \:instant}[/tex]Formula to be used :-[tex]\sf\blue{K.E. = \dfrac{1}{2} mv^{2}}[/tex]Where,
K.E. = Kinetic energy possessed by the bodyM = Mass of the bodyV = Velocity of the bodySolution :-[tex]\to\:\:\sf\red{K.E. = \dfrac{1}{2}mv^{2}}[/tex]
[tex]\to\:\:\sf\orange{5000 = \dfrac{1}{2} \times 100 \times v^{2}}[/tex]
[tex]\to\:\:\sf\green{5000 = 50 \times v^{2}}[/tex]
[tex]\to\:\:\sf\blue{\dfrac{5000}{50} = v^{2}}[/tex]
[tex]\to\:\:\sf\purple{100 = v^{2}}[/tex]
[tex]\to\:\:\sf\red{\sqrt{100} = v}[/tex]
[tex]\to\:\:\sf\orange{ 10 = v}[/tex]
[tex]\to\:\:\bf\pink{v = 10\:m/s}[/tex]
Velocity of the vehicle at the instant is [tex]\bf\green{10\:m/s}[/tex]HELP!!!!This question is typical on some driver's
license exams: A car moving at 49 km/h skids
12 m with locked brakes.
How far will the car skid with locked brakes
at 122.5 km/h? Assume that energy loss is
due only to sliding friction.
Answer in units of m.
Answers
Answer:
d=75 m
Explanation:
Before Skidding
[tex]v^2-v_o^2=2ad[/tex]
[tex]0^2-49^2=2a(12)[/tex]
After Skidding
[tex]v^2-v_o^2=2ad[/tex]
[tex]0^2-122.5^2=2ad[/tex]
[tex]\frac{49^2}{122.5^2}=\frac{12}{d}[/tex]
[tex]d=75 m[/tex]
Hope it helps
A 20 kg wagon is rolling to the right across a floor. A person attempts to catch and stop the crate and applies a force of 70 N, 180.0 on it. If the coefficient of friction is 0.18, calculate the deceleration rate of the wagon as it is caught.
Answers
Answer:
1.736m/s²
Explanation:
According to Newton's second law;
[tex]\sum F_x = ma_x\\[/tex]
[tex]Fm - Ff = ma_x\\[/tex] where;
Fm is the moving force = 70.0N
Ff is the frictional force acting on the body
[tex]Ff = \mu R\\Ff = \mu mg\\[/tex]
[tex]\mu[/tex] is the coefficient of friction
m is the mass of the object
g is the acceleration due to gravity
a is the acceleration/deceleration
The equation becomes;
[tex]Fm - Ff = ma_x\\Fm - \mu mg = ma\\[/tex]
Substitute the given parameters
[tex]Fm - \mu mg = ma\\70 - 0.18(20)(9.8) = 20a\\70-35.28 = 20a\\34.72 = 20a\\a = \frac{34.72}{20}\\a = 1.736m/s^2\\[/tex]
Hence the deceleration rate of the wagon as it is caught is 1.736m/s²
If a ball that is freely falling has attained a velocity of 19.6 m/s after 2 seconds,
what is its velocity 5 seconds later?
Answers
Answer:
68.6 m/s
Explanation:
Recall that the velocity formula to use for accelerated motion due to gravity (g) is:
vf =vi + g * t
so if 19.6 m/s is the initial velocity for the free falling object, then, 5 seconds later under the acceleration of gravity (g) :
vf = 19.6 + 9.8 * (5) = 68.6 m/s
convert 100 Newton into dyne
Answers
Answer:10000000
Explanation:
A metal box of weigh 20 N rests on its 1 m by 0.6m side on floor. How
much is the pressure exerted by the metal box on the floor? Take g=
10 m/s
Answers
Answer:
P = 33.33 [Pa]
Explanation:
The pressure can be calculated by the relationship of the force over the area.
[tex]P =F/A[/tex]
where:
F = force = 20 [N]
A = area = 1 x 0.6 = 0.6 [m²]
Now replacing:
[tex]P=20/0.6\\P=33.33 [Pa][/tex]
How can you prove that the potential energy of a stretched spring turns into kinetic energy when you release the spring?
Answers
Potential energy+Kinetic energy=Total energy
When you release a spring the velocity increases, therefore the kinetic energy increases ke=1/2*mv^2 and the displacement decreases therefore the potential energy decreases pe=1/2*kx^2.
A car goes around a circular track at 30 m/s. If the radius of the curve is 90 m, what is the period of the car's revolution around the track?
Answers
Answer:
18.9s
Explanation:
Using the formula;
ω = v/r
Where;
ω = angular velocity (rad/s)
v = linear velocity (m/s)
r = radius of the circular track (m)
According to the given information, v = 30m/s, r = 90m
ω = v/r
ω = 30/90
ω = 3/9
ω = 0.3333 radians/seconds.
Since ω = 2π/T
Where;
π = 3.142
T = period (s)
ω = angular velocity
0.333 = 2 × 3.142/T
T = 2 × 3.142/0.333
T = 6.284/0.333
T = 18.87s
T = 18.9s
A 0.6 m length of current carrying wire is placed in a uniform magnetic field oriented perpendicularly to the wire. The current is 4 A and the magnitude of the magnetic field is 10 T. What is the force on the wire?
a. 0 N.
b. 2.4 N.
c. 6 N.
d. 24 N.
e. 30 N.
Answers
Answer:
D. The force on the wire is 24 N.
Explanation:
Given;
length of the wire, L = 0.6 m
current in the wire, I = 4 A
magnitude of the magnetic field, B = 10 T
The fore on the wire is calculated as;
F = BILsinθ
where;
θ is the angle of inclination of the wire on magnetic field = 90°
F = (10)(4)(0.6)(sin 90°)
F = 24 N
Therefore, the force on the wire is 24 N.
What is the name for family labeled #4 (Yellow)?
#3
#5
#2
#
341 sud-
lasa 1
17:55
Alkaline Earth Metals
Metalloids
Transition Metals
Alkali Metals
Answers
Answer:
transition metals im sorry if this was too late
what do scientists compare to make sure they classify an organism correctly?
A: Other organisms
B:Taxonomic charts
C: DNA strands
D:Skeletons
Answers
Answer:
Explanation:
I think is B
Determine the acceleration that results when a 12 N net force is applied to a 3 kg object.
Answers
Heya!!
For calculate aceleration, let's applicate second law of Newton:
[tex]\boxed{F=ma}[/tex]
⇒ Being:
→ F = Force = 12 N
→ m = Mass = 3 kg
→ a = aceleration = ?
Lets replace according formula and leave the "a" alone:
[tex]12\ N = 3\ kg * \textbf{a}[/tex]
[tex]\textbf{a} = 12\ N / 3\ kg[/tex]
[tex]\textbf{a} = 4\ m/s^{2}[/tex]
Result:
The aceleration of the object is of 4 m/s²
What do we call the material such as air that light travels through
Answers
Answer:
Transparent or Translucent
Explanation:
Compute the specific heat capacity at constant volume of nitrogen (N2) gas. The molar mass of N2 is 28.0 g/mol.
Answers
Answer:
724.3J/Kg.K
Explanation:
CHECK THE COMPLETE QUESTION BELOW
Compute the specific heat capacity at constant volume of nitrogen (N2) gas.and compare with specific heat of liquid water. The molar mass of N2 is 28.0 g/mol.
The specific heat capacity can be computed by using expression below
c= CV/M
Where c= specific heat capacity
M= molar mass
CV= molar hear capacity
Nitrogen is a diatomic element, the Cv can be related to gas constant with 5/2R
Where R= 8.314J/mol.k
Molar mass= 28 ×10^-3Kg/mol
If we substitute to the expression, we have
c= (5R/2)/(M)
=5R/2 × 1/M
=(5×8.314) /(2×28 ×10^-3)
=724.3J/Kg.K
Hence, the specific heat capacity at constant volume of nitrogen (N2) gas is
724.3J/Kg.K
The specific heat of liquid water is about 4182 J/(K kg) which is among substance with high specific heat, therefore specific heat of Nitrogen gas is 724.3J/Kg.K which is low compare to that of liquid water.
As a bicycle is ridden west in a straight line with decreasing speed,the acceleration of the bicycle must be
Answers
Answer:
Decreasing
Hope this helps! :)
n
Question 4
1 pts
A bus travels on an interstate highway at an average speed of 90 km/hrs. How far does it take to travel
in 30 mins? The distance equals speed times time, or d = st.
O 45 km
O 98 Km
O 56 km
O 432 Km
Answers
[tex]d = s \times t \\ d = 90 \times \frac{30}{60} \\ d = 90 \times \frac{1}{2 } \\ d = 45km[/tex]
a car traveling at 28.4 m/s undergoes a constant deceleration of 1.92 m/s2 when the breaks are applied. How many revolutions does each tire make before the car comes to a stop
Answers
Complete Question
a car traveling at 28.4 m/s undergoes a constant deceleration of 1.92 m/s2 when the breaks are applied. How many revolutions does each tire make before the car comes to a stop? Assume that the car does not skid and that each tire has a radius of 0.307 m. Answer in units of rev.
Answer:
The value is [tex]N = 109 \ rev[/tex]
Explanation:
From the question we are told that
The speed of the car is [tex]u = 28.4 \ m/s[/tex]
The constant deceleration experienced is [tex]a = 1.92 \ m/s^2[/tex]
The radius of the tire is [tex]r = 0.307 \ m[/tex]
Generally from kinematic equation we have that
[tex]v^2 = u^2 + 2as[/tex]
Here v is the final velocity which is 0 m/s
So
[tex]0^2 = 28.4^2 + 2 * 1.92 * s[/tex]
=> [tex]s = 210.04 \ m[/tex]
Generally the circumference of the tire is mathematically represented as
[tex]C = 2 \pi r[/tex]
=> [tex]C = 2 * 3.142 * 0.307[/tex]
=> [tex]C = 1.929 \ m[/tex]
Generally the number of revolution is mathematically represented as
[tex]N = \frac{ s}{C}[/tex]
=> [tex]N = \frac{210.04}{1.929}[/tex]
=> [tex]N = 109 \ rev[/tex]
John decided to cycle to his friend's house at a speed of 5km/h and the journey took 2
hours. How far did John cycle?
Answers
Answer:100 miles
Explanation:
Answer:
10 Km
Explanation:
He is going 5km per hour and he arrived at his friend's house in 2 hours. You multiply 5 by 2 and you get 10.
cell graphic organizer 1-20
Answers
The show waterbell Nowing into a pool of water
Which statement des describes the energy of the objects in the drawing?
The pool of water has more kinetic energy and the falling water has more potential energy.
The falling water has potential energy and the rock over which it flows has kinetic energy
The water has potential energy at the top of the waterfall and increasing kinetic energy as it falls.
The water at the top of the fall has kinetic energy that becomes potential energy as it falls into the pool.
Answers
Answer:
The water has potential energy at the top of the waterfall and increasing kinetic energy as it falls.
Explanation: