Midterm Exam 2: Work and energy, momentum and collisions, rotational motion

Question 1

If there is a nonzero net torque on a system, what is definitely true?

Answer 1

Its angular momentum is not constant.

[torque = dL/dt]

Question 2

A ball drops some distance and loses 30 J of potential energy. If the effects of air resistance are included, how much kinetic energy did the ball gain?

Answer 2

Less than 30 J.

Question 3

A mass m slides slowly down a gently sloping hill through a total vertical distance h. If there is no friction, what is the work done by gravity?

Answer 3

mgh

[Wc = -∆U = -(mghi - mghf) = mghf

Question 4

A mass m slides slowly down a gently sloping hill with lots of friction through a total vertical distance h. What is the work done by gravity?

Answer 4

mgh

Question 5

Describe the relationship between the final kinetic energy and the initial kinetic energy in an inelastic collision.

Answer 5

The final total kinetic energy is less than the initial total kinetic energy.

Question 6

The path of a point on a rigid body that is rotating but not translating is __________.

Answer 6

a circle

Question 7

What is true about potential energy?

Answer 7

Potential energy depends on the position/configuration of objects, it cannot have a universally defined zero level, and, in the case of a spring, it is related to the square of the displacement from the equilibrium position.

Question 8

Considering all forms of energy including internal energy, when is the sum of the kinetic and potential energies of a system necessarily constant?

Answer 8

If the system is isolated and subject to conservative forces only, then ∑K + ∑U = constant.

Question 9

The change in kinetic energy of a system is always equal to __________.

Answer 9

the sum of the conservative and nonconservative work done on the system

Question 10

Why does a brick wall coated in cotton balls feel softer than a bare brick wall if you crash into it?

Answer 10

The momentum change occurs over a longer time for the case of the cotton.

Question 11

Two billiard balls collide elastically and bounce out along the same line they came in on. Which of the following would increase the outgoing speed of ball 2?

Answer 11

An increase in the incoming speed of ball 1 would increase the outgoing speed of ball 2.

Question 12

Why can a figure skater twirl around with such a high frequency after starting out at a lower frequency?

Answer 12

She can start spinning and then reduce her moment of inertia.

Question 13

On a frictionless warehouse floor, a 40-kg box slides with a speed of 4.0 m/s and collides with another box which has a mass of 50 kg and is initially moving at 4.0 m/s in a perpendicular direction to the first box. When they collide they stick together and slide off together. With what speed do they exit the collision point? How much kinetic energy turns into another form of energy in this collision?

Answer 13

v = 2.84 m/s
E(lost) = 358 J

Question 14

A mass m is sliding down the road, initially moving at v(i). It then runs into a giant, initially uncompressed horizontal spring with a spring constant of k. What is the maximum compression of the spring neglecting friction and the mass of the spring, in terms of m, v(i), and k?

Answer 14

x = v(i)*√(m/k)

Question 15

A 50-kg snowboarder starts from rest at the top of a slope. The frictional force with the ground is a constant 20 N. After going 150 m down a gentle hill with a constant slope of 5.7deg, what is the snowboarder’s speed? How much work is required to bring the snowboarder to a complete stop?

Answer 15

v = 13.1 m/s
W = 4920 J

Question 16

An object is sliding across a smooth horizontal floor with a constant speed v(i), but then slides onto a rough patch where the coefficient of kinetic friction is µ. It slows to a complete stop over a distance d. Use work-energy considerations to get the speed v(i) in terms of d, µ, and g. Use Newton’s second law and motion at constant acceleration to get the speed v(i) in terms of d, µ, and g.

Answer 16

v(i) = √(2µgd)

Question 17

A meteor with mass 5.3E6 kg enters the Earth’s atmosphere and blows up, releasing 2.1E15 J of energy. If the explosion happens very quickly so that the potential energy does not change during it, what was the speed of the meteor right before the explosion? Given this velocity, assuming it is the speed with which the meteor entered the atmosphere at a height of 25 km, and that there was no work done on the meteoroid by anything other than gravity in its journey toward Earth, what was the speed of the meteoroid when it was very far from the Earth? (M(E) = 5.97E24 kg, R(E) = 6.4E6 m)

Answer 17

v = 2.8E4 m/s
v = 2.6E4 m/s

Question 18

A ball of mass 0.1 g moving at 10 m/s collides head-on with an initially stationary ball of mass 0.09 g on a pool table. The collision is elastic. What is the speed and direction of each ball immediately after the collision? (The initial direction of the first ball’s movement is in the +x direction.)

Answer 18

v(1f) = +0.5 m/s
v(2f) = +10.5 m/s

Question 19

A mass m hangs on a rope wrapped around a frictionless pulley of mass M and radius R. The pulley is basically a cylinder, so the moment of inertia is 1/2 MR^2. Assuming no friction, what is the angular acceleration α of the pulley in terms of g, R, m, and M?

Answer 19

α = g/R(1+(M/2m))

Question 20

A bicycle wheel with mass 1 kg and radius 0.2 m starts from rest and accelerates under a constant torque of 0.3 Nm for 8 s. The moment of inertia of this wheel is I = MR^2. What is the wheel’s final angular velocity? Considering that is has both translational and rotational kinetic energy, how much work would it take to stop the wheel at this time? If some tar (0.5 kg) suddenly stuck to the wheel, what would the new angular velocity be?

Answer 20

ω = 60 rad/s
K = 144 J
ω(tar) = 40 rad/s

Question 21

A stationary sign is hung vertically from the end of a horizontal bar which is supported by a cable with restraining forces being provided by a wall to which the bar is attached (F(w)) and the tension in the table (T). The total length L of the horizontal bar is 60 cm and the distance d from the wall to the cable attachment point on the bar is 50 cm. The angle θ between the cable and the horizontal bar is 30deg.

Find the magnitude of the force T and the horizontal and vertical components of the force F(w).

Hint: Start with taking the torques about the point where the cable attaches to the bar. This will give you F(wy). Then consider the y forces to get T. Then consider the x forces to get F(wx).

Answer 21

F(wy) = 20 N
T = 240 N
F(wx) = 208 N