A 100-kg box is sliding down a frictional surface with an acceleration of -2.0m/s².
Determine the magnitude of the friction force on the object.

Answer:

Vx = 150 * cos 53 = 90.3 m/s     horizontal speed

Vy = 150 * sin 53 = 120 m/s      vertical speed

t1 = 120 / 9.8 = 12.2 sec       time to reach vertical height  (vy = 0 at apex)

H1 = 1/2 g t^2 = 9.8 / 2 * 12.2^2 = 729 m    height risen above cliff

729 + 405 = 1134 m      total height above striking point

H = 1/2 g T^2          where T is time to fall 1134 m

T = (2 * 1134 / 9.8)^1/2 = 15.2 sec

T + t1 = 15.2  + 12.2 = 27.4 sec total time in air

Sx = Vx * 27.4 = 90.3 * 27.4 = 2470 m   total horizontal distance

Answer:

1.22 m/s² (3 s.f.)

Explanation:

Draw a diagram modelling the given situation (see attachment).

Given values:

As the pulling force is at an angle to the plane (ground), resolve the force into components parallel and perpendicular to the plane.

Resolving vertically (↑) to find the Normal Reaction, R:

[tex]\begin{aligned}\implies R+82.2 \sin 64^{\circ}&=14g\\R&=14g-82.2 \sin 64^{\circ}\end{aligned}[/tex]

The frictional force takes its maximum value when an object starts to move (or is on the point of moving):

[tex]\boxed{F_{\text{max}}= \mu R}[/tex]

where R is the Normal Reaction and μ is the coefficient of friction.

Using F = μR to find the Frictional Force, F:

[tex]\begin{aligned}\implies F &= 0.3\left(14g-82.2 \sin 64^{\circ}\right)\\ & =0.3\left(14(9.8)-82.2 \sin 64^{\circ}\right)\\& =0.3\left(137.2-82.2 \sin 64^{\circ}\right)\\ & = 41.16-24.66\sin 64^{\circ}\end{aligned}[/tex]

Newton's second law states that the overall resultant force acting on a body is equal to the mass of the body multiplied by the body’s acceleration:

[tex]\boxed{F_{\text{net}}=ma}[/tex]

Resolving horizontally (→) using Newton's second law of motion to find acceleration:

[tex]\begin{aligned}\textsf{Using} \quad F_{\text{net}}&=ma\\\\\implies 82.2 \cos64^{\circ}-(41.16-24.66\sin 64^{\circ})&=14a\\17.0383694...&=14a\\a&=\dfrac{17.0383694...}{14}\\a&=1.21702638...\\a&=1.22\;\sf m/s^2\;(3\;s.f.)\end{aligned}[/tex]

Therefore, the acceleration of the box is 1.22 m/s² (3 s.f.).

Answer:

4500 N

Explanation:

Bc f is equal to mass times acceleration and the acceleration is 60

If a 75 kg student drives a 650 kg car, then the car starts from rest and accelerates to 60 m/s in 8 seconds, then the applied force on the car would be 5437.5 Newtons.

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

The mathematical expression for Newton's second law is as follows

F = m × a

As given in problem an If a 75 kg student drives a 650 kg car, the car starts from rest and accelerates to 60 m/s in 8 seconds.

The acceleration of the car = 60 / 8

                                             = 7.5 m / s²

The force applied on the car = 725 × 7.5

                                                = 5437.5 Newtons

Thus,  the applied force on the car would be 5437.5 Newtons.

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Given

Initial speed, u=45 m/s

Acceleration

Time taken, t=4 sec

To find

The final speed

Explanation

Let the speed he be going in be v

Thus,

Conclusion

The velocity he is going in is 13 m/s.

By wearing the helmet, the time isextended during which the change in momentum of the body takes place during the crash.

This increase in time for the force acting on the body will decrease the impact of force on the body.

In the given graph, the value of force on the head is less and time taken is more in the first graph.

Thus, the first graph (1) represent the wearing helmet case.

The force on the head is more and time is less in the second case.

Thus, the second graph (2) represents the without helmet case.

The spring constant is  400 N/m and The mass which would produce an extension of 3.0 cm is 0.0459 kg.

Here we are dealing with a problem related to hook's law which states that the force required to expand or compress a spring by a few distances is corresponding to that distance. This can be expressed scientifically as F= -kx, where F is the force connected to the spring and x is the displacement of the spring, with negative esteem illustrating the displacement of the spring once it is extended; and here k is the spring constant.

For the first case, we are given the force applied which is 20 N, and the extended length which is 5cm =0.05 m,

So the spring constant will be, k= F/x=  20/0.05 = 400 N/m

For the second  case we are given that the spring constant which is 15 N/m  and the extension is 3.0 cm =0.03 m.

Since we know F= mg ( where g is the acceleration due to gravity )

So the hanging mass, will be

=>F= kx

=>mg=kx

=>m=kx/g

      =15 x0.03/9.8

     = 0.0459 kg

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The equation which represent the velocity, if the satellite is moved to an orbital radius of 5r is V = V/[tex]\sqrt\\5[/tex].

Orbital velocity or orbital speed is the minimum velocity a body must maintain to stay in an orbit. Due to the inertia of a moving body, the body has the tendency to move on in a straight path.

It is given that the radius is 5r

To find out the equation which represent the velocity if the satellite is moved to an orbital radius of 5r.

Mathematically, the orbital velocity is calculated by the formula:

V = [tex]\sqrt{GM}[/tex]/r

where, V = orbital velocity,

G = gravitational constant

M = mass of a satellite

r = radius

Substituting the value of r in this equation, we have:

V = [tex]\sqrt{GM}[/tex]/r

V = 1/ [tex]\sqrt{5}[/tex] ×  [tex]\sqrt{GM}[/tex]/r

V = [tex]\sqrt{GM}[/tex]/r

Therefore,

V = 1/ [tex]\sqrt{5}[/tex]  × V

V = V/[tex]\sqrt{5}[/tex]

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The final velocity V is 40 km/h.

The final velocity V.

Mass of wagon m = 1000 kg

Initial velocity of wagon v = 50 km/h

Mass dropped velocity M = 250 kg

The final velocity =V

Initial system linear momentum [tex]P_{i}[/tex] = mv

=1000*50

=5*[tex]10^{4}[/tex] kg km/h

The system with the final velocity (wagon + mass dropped) be V .

Final system linear momentum [tex]P_{f}[/tex] = (m + M) V

=(1000+250)V

=1250 V

Basic principle of conservation of linear momentum,

[tex]P_{f}[/tex] = [tex]P_{i}[/tex]

1250V=5*[tex]10^{4}[/tex]

V=[tex]\frac{5*10^{4} }{1250}[/tex]

V= 40 km/h

So, the final velocity V is 40 km/h.

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Given:

The lamp draws the current is

The voltage supplied by the generator is

The time for which energy converted is

Explanation:

(a)

The power delivered by the generator is given by

Plugging all the values in the above equation, we get

The power delivered by the generator is

(b)

Energy is converted by the electric lamp is given by

Plugging all the values in the above relation, we get

Thus, the electric energy convert by the lamp is

1) Solid ,whose molecules are compactly arranged . so ,letter N  

2) liquid state -the state in which molecules are arranged neither too compact nor loose . SO, letter O is pure liquid

3) letter Q is a pure gas

The quantity of heat energy needed to convert a substance from a solid to a liquid is known as the heat of fusion. Enthalpy of fusion is another name for it. Joules per gram (J/g) or calories per gram (Cal/g) are typically used as its units. The solution to this example problem shows how to determine how much energy is needed to melt a sample of water ice.

The quantity of heat energy required to convert solid stuff into liquid is known as the heat of fusion (melting.)

Q = mHf is the formula for calculating heat of fusion.

The temperature is not a factor in the equation or the computation because matter does not truly change temperature when it changes states.

Heat of fusion is usually a positive value, with the exception of when melting helium.

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Increasing his acceleration will impact his velocity and rate of displacement covered in that as the speed increases due to the increased rate of acceleration, the rate of air resistance also increases.  

Air resistance is a force created by air. When an item moves through the air, the force operates in the opposite direction.

When a diver descends, the force of air resistance acts to counteract the force of gravity. As the skydiver falls faster and faster, the quantity of air resistance grows until it equals the magnitude of gravity's force.

A balance of forces is achieved when the force of gravity equals the force of air resistance, and the skydiver no longer accelerates. The skydiver reaches what is known as terminal velocity.

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The magnitude of the earth’s acceleration toward the apple with a mass of 0.38 kg is 6.2 × 10⁻²⁵ m/s².

Gravity is a fundamental force which is responsible for causing mutual attraction between all the things with mass or energy.

The gravitational force can be calculated by the formula:

F = m.a

where, F = force

m = mass of an object

a = acceleration of the object

Here, the mass of the apple, m = 0.34 kg

The acceleration of the apple towards the earth's surface (a) = 9.8 m/s²

The mass of the Earth, M = 5.98 × 10²⁴ kg

Now, by applying Newton's Law of the motion,  

The magnitude of the force on the apple due to Earth is can be calculated as:

F = m × a

F = 0.34 × 9.8

F = 3.724 N

According to the Newton's third law of motion, the apple must exert an equal but opposite force on Earth.

So, the magnitude of the force on Earth due to the apple will be:

F = 3.724 N

Let the magnitude of the earth’s acceleration towards the apple be 'A' m/s².

Thus, the magnitude of the earth’s acceleration towards the apple will be given by:

F = MA

M = mass of the Earth

A = acceleration of the Earth

3.724 = [5.8 × 10²⁴] × A

A = 3.724 / [5.8 × 10²⁴]

A = 0.6227 × 10⁻²⁴

A = 6.2 × 10⁻²⁵ m/s²

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Answer:

Therefore the friction Force is 65 N.

Explanation:

Look at the image above.

The frictional force of the rubber block is 63.7N.

Friction is defined as a force that opposes the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are many types of friction such as dry friction which is defined as the force that opposes the relative lateral motion of two solid surfaces in contact.

This friction force is directed in the opposite direction to the motion of the object itself because the friction described so far between surfaces in relative motion is called kinetic friction.

For above given information,

mass of the block, m =10kg

coefficient of friction, µ=0.65

f=coefficient of the friction ×normal= µ*R

R= normal =mg = 9.8×10=98N

So, f =0.65×98=63.70N

≈65N(when g is taken as 10m/s²)

Thus, the frictional force of the rubber block is 63.7N.

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The cargo while it was accelerating at a distance of  0.602 meters.

Acceleration is the name we give to any system wherein the speed changes. on the grounds that speed is a pace and a direction, there are only two approaches so that you can boost up.

Velocity is the rate of change of displacement. Acceleration is the price of alternate velocity. velocity is a vector quantity because it consists of both significance and direction. Acceleration is likewise a vector quantity as it's far simply the charge of alternate velocity.

initial velocity = 55 m/hr

                   = 55/60× 60 m/sec

                    = 0.0152 m/sec

final velocity = 16 mi/hr

                      = 16/3600

                     = 0.0044 m/sec

time = 3.2 sec

V = u -  at

a = ( U - V )/t

  =  (0.0152 - 0.0044)/t

  = 0.0108 m/sec²

S = ut + 1/2at²

   =  0.0152 × 3.2 sec + 1/2 × 0.0108 m/sec² ×  (3.2)²

   = 0.0486 + 0.553

   = 0.602 meter.

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The correct answer is option C, 0.50 N to the left.

Given,

The charges,

q₁=5×10⁻⁶ C

q₂=4.0×10⁻⁶ C

q₃=10.0×10⁻⁶ C

The distance between the 1st charge and the second charge, r₁=20 cm=0.20 m

The distance between 2nd charge and the 3 rd charge, r₂=30 cm=0.30 m

As all the charges have the same sign, the nature of the force is repulsive. Thus the force applied by the q₂ is directed to the left. And the force applied by the charge q₃ is pointed to the right.

From Coulomb's law, the net electrostatic force on q₂ is given by,

On substituting the knwon values,

Thus the magnitude of the net electrostatic force on the charge q₂ is 0.5 N

As the force to the left is greater than the force to the right, the net force will be directed to the left.

Therefore the correct answer is option A, 0.50 N to the left.

Since there is a wind speed of 50 km/h to the west, this speed needs to be compensated by the heading of the plane.

If we decompose the plane speed, one component will be used to cancel out the wind speed:

To find the orientation theta, we can calculate the east component of the plane speed and equate it to the wind speed:

Now, let's calculate the south component:

Calculating the required time of flight, we have:

Therefore the orientation is 9.59° east of south and the time required is 8.45 hours.

If an electron travels 2.68 m in 6.11 × 10^-8 s, it will travel at a speed of 43.86 * [tex]10^{8}[/tex] cm / s

v = d / t

v = Velocity

d = Distance

t = Time

d = 2.68 m

t = 6.11 * [tex]10^{-8}[/tex]

v = 2.68 / 6.11 * [tex]10^{-8}[/tex]

v = 0.4386 * [tex]10^{8}[/tex] m / s

v = 0.4386 * [tex]10^{8}[/tex] * 10² cm / s

v = 43.86 * [tex]10^{8}[/tex] cm / s

One meter is equal to 100 centimeters. So in order to convert a meter value into centimeter, multiply the meter value by 100 or 10².

Therefore, the electron travels at 43.86 * [tex]10^{8}[/tex] cm / s

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W0e are asked to determine the frequency of a sound given its velocity and wavelength. To do that we will use the following formula:

Where:

Now, we solve for the frequency by dividing both sides by the wavelength.

Now, we substitute the values:

Solving the operations:

Therefore, the frequency is 40 Hz.

There are six half lives that have passed within 34,200 years. When we assume that we have some of the products present initially, then we overestimate the age of the sample.

The half life is the time taken to obtain only half of the number of atoms that were originally present in the radioactive material. We know that living things do contain the carbon- 14 isotope together with the carbon - 12 isotope in the substance. When the organism dies, the carbon - 14 which is radioactive begins to decay and its half life could be used to estimate the age of the sample as we know.

Given that after each half life, we have only half of the original amount that remains. We would have 1/64 of the original amount left after six half lives and this means that 34,200 years have passed.

If we  the daughter product of carbon-14 is present in the sample when it forms (even before any radioactive decay happens), then we would over estimate the  age of the sample.

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Given,

The radius of the wheel, r=0.300 m

The mass of the wheel, m=1.47 kg

The initial angular frequency of the wheel, f=4.00 rev/s

The time it takes for the wheel to come to a stop, t=56.4 s

The final angular velocity of the wheel, ω=0 rad/s

The initial angular velocity of the wheel is

From the equation of motion,

Where α is the angular acceleration of the wheel.

On substituting the known values,

The moment of inertia of the wheel whose mass is concentrated on the rim is given by,

The torque applied by the friction is given by,

On substituting the known values,

The negative sign of the torque indicates that the torque is applied to the wheel in the direction opposite to the direction of rotation of the wheel.

Thus the magnitude average torque due to frictional force is 0.06 Nm

The correct option is option (D)  occur in Nashville occur at the same coordinates.

In general proper time is the time interval  between two events as measured by an observer who sees the event occur at the same position.

In geometry, a coordinate system is a device that makes use of one or more numbers, or coordinates, to uniquely determine the location of the points or different geometric factors on a manifold which includes Euclidean area.

Math coordinates discover the vicinity of a factor on a graph or map. The ordered pair, (x, y) is the cope with of the factor. The Cartesian coordinate gadget is the graph used to locate the point. The graph is split up into four quadrants.

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The time taken for the bullet moving with a speed of 600 m/s to hit a target  200 meters away is 3.33 s.

Time is the measured or measurable period during which an action, process, or condition exists or continues.

To calculate the time it takes the bullet to hit the target, we use the formula below.

Formula:

Where:

Make t the subject of the equation

From the question,

Given:

Substitute these values into into equation 2

Hence, the time it will take to hut the target is 3.33 seconds.

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Answer:

III only

Explanation:

The net vertical force is equal to 0 because the block is not moving up. Then, we can write the following equation

Fnet = N + Fsinθ - mg = 0

Where Fsinθ is the vertical component of the force F. Solving for the normal force N, we get:

N = mg - Fsinθ

Therefore, the normal force is not equal to the weight and the normal force is not mgcos(θ)

However, the horizontal component of F is Fcos(θ). So, the answer is

III only.

Set of equation which is true for the situation is

c) 2SA = SB  and 2BA=BB

Force applied perpendicular to the surface of an object per unit area is called pressure

SI unit of pressure is one newton per square meter (N/m2).

Given, length = 3 foot, width= 1 foot and height = 1 foot

1foot = 0.305m

Volume of tank A = 3*0.305*0.305*0.305

= 0.085

density of water= 1000kg/m^3

Pressure= 1000kg/m^3 *gravity * height

=1000kg/m^3 * 9.8 m/s^2* 0.305

=2989 N

Force exerted by water at bottom= P * A

                                                        = 2989*0.085

                                                         =254.065 Nm^2

similarly, for tank B

Given ,length = 6 foot, width =1 foot and height= 1foot

Volume of tank B = 6*0.305*0.305*0.305

                               =0.17

pressure= 1000kg/m^3 * 9.8m/s^2 * 0.305

               = 2989 N

Force exerted by water at bottom = P*A

                                                         = 2989 * 0.17

                                                          =508.13 Nm^2

Hence proved that pressure exerted by tank B is twice that of tank A.

And same goes for pressure exerted on the side of the tank.

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Just because there is a relationship between two behaviors does not mean that one causes the other. Option A.

Natural observation is a research method that observes objects in their natural environment. This approach is commonly used by psychologists and other social scientists. It is a process of deep reflection, questioning, and evidence evaluation. A study in which researchers look for relationships between people's demographic neighborhood and their level of prejudice.

Psychologists use this because it is the most objective method known to produce reliable insights. The science of behavior and mental processes. It attempts to describe and explain aspects of human thinking feeling perception and behavior. Naturalistic observation is a method of observation that involves observing people's behavior in environments in which they normally occur. Laboratory Observation observing behavior in a more artificial environment focusing on a small number of carefully defined behaviors.

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3.7996 seconds are needed to accelerate it.

acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even while the speed is constant.

So we have u= 0m/s, v=15m/s, s= 200m

So,2as= v^2-u^2

A= V^2 - U^2/2s

= 225/400

=0.5625 m/s^2

V=u + a*(t^2)

15=0+0.5625(t^2)

15-0.5625= t^2

=14.4375=t^2

root14.4375= root(t)

Time= 3.7996 seconds

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Linear velocity (V) = r* w

where:

r = radius = diameter/2= 0.35 /2 = 0.175 m

w= angular velocity = rpm = 2500 = 2500/60 = 125/3 rps

1 revolution = 360° = 2pi rad/s = 125/3 2pi rad/s

= 261.8 rad/s

v = 0.175 m * 261.8 m/s = 45.8 m/s

The x-component of the vector is determined as -16.24 m.

The x-component of a vector is the vector component measured along x - direction. It is the vector acting in the x-coordinate.

The magnitude of x -component of a vector is given by the following formula as shown below;

Vₓ = V cosθ

where;

Vₓ = 148 m x cos(-96.3)

Vₓ = -16.24 m

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Answer:

Y= -147

X= -16.24

Explanation: