Q: A ballistic pendulum: a bullet of mass $$m is $$shot with speed $$v$$ into a block of mass $$M$$ hanging from a string of length $$L. $$The bullet sticks in the block and the block swings up to an angle $$\theta. $$What is the speed of the bullet?

$$\frac{m+M}{m} \sqrt{2gL(1-\cos\theta)}$$

Question 1

Three point masses, each of mass $$m$$, are connected by rigid massless rods as shown in the diagram. Where is the center of mass of this object in the given coordinates $$(x, y)$$?

Accepted Answer

$$( \frac{2}{3}a, \frac{1}{3}a )$$

Question 2

A bicycle wheel of mass $$M$$ and radius $$R$$ starts from rest and rolls down a hill of height $$h$$ without slipping. What is its speed at the bottom? (Moment of inertia $$I_{	ext{wheel}} = MR^2$)

Accepted Answer

$$\sqrt{2gh}$$

Question 3

A box of mass $$m$$ slides along a horizontal frictionless track at speed $$v. It $$hits a spring of spring constant $$k$$ and comes momentarily to rest. How far was the spring compressed?

Accepted Answer

$$\sqrt{\frac{m}{k}} v$$

Question 4

A meteoroid of mass $$m$$ and velocity $$\vec{v}_1 = 1000\,\hat{i} + 1000\,\hat{j} m/s $$collides with an identical meteoroid of mass $$m$$ and velocity $$\vec{v}_2 = 1000\,\hat{i} - 1000\,\hat{j} m/s. $$The two stick together. What is their final velocity?

Accepted Answer

$$(1000\,\hat{i}) m/s$$

Question 5

You are using a wrench to loosen a bolt. You apply a force $$F = 2.5 N to $$create a torque of $$1.25 N$$·m. How long is the wrench?

Accepted Answer

$$0.2 m$$

Question 6

From the top of a building, object 1 with mass $$m is $$thrown straight downward, and object 2 (also with mass $$m) is $$thrown upward at an angle of $$60^\circ. $$Both are thrown with the same speed. Compare the speeds with which the objects hit the ground.

Accepted Answer

$$v_1$$ = $$v_2$$

Question 7

A roller coaster starts at rest from the top of a hill of height $$h$$, coasts down, and then does a loop-the-loop of radius $$R. If $$the riders should feel weightless at the top of the loop, at what height should the hill be? Ignore friction.

Accepted Answer

$$\frac{5}{2}R$$

Question 8

A firework of mass $$24 kg $$moving vertically upward at $$v_i = 100 m/s $$explodes into three pieces of $$8 kg $$each. Two pieces fly off at $$30^\circ$$ angles with speed $$100 m/s. $$What is the speed $$v_2 of $$the third piece?

Accepted Answer

$$200 m/s$$

Question 9

A superball of mass $$m is $$thrown at a wall with speed $$v_i$$ and bounces directly back at the same speed. What is the magnitude of the impulse on the superball?

Accepted Answer

$$2m v_i$$

Question 10

Refer to the diagram with three springs labeled A, B, and C, each holding a different mass. Which spring has the largest spring constant?

Accepted Answer

Spring A

Question 11

Two forces are applied to a door as shown, one at the middle and one at the end. $$F_1 = 20$ N and F_2$ = 20 N. $$The door is $$100 cm $$wide. What is the net torque on the door?

Accepted Answer

$$10 N$$\cdot m

Question 12

A person is holding a spinning bicycle wheel and is sitting in a chair that is free to rotate. When they flip the bicycle wheel over, what happens and why?

Accepted Answer

The person starts to spin due to conservation of angular momentum.

Question 13

You drop a ball of mass $$m$$ from a height $$h. $$How fast is it going when it hits the ground?

Accepted Answer

$$\sqrt{2gh}$$

Question 14

A box of mass $$m is $$pulled across the ground with a horizontal force $$F_{	ext{pull}} = Cx^3$, where C$ is a constant, from x=0$ to x=d$. What is the work done by F$$_{	ext{pull}}$$?

Accepted Answer

$$\frac{C d^4$}{4}$$

Question 15

A truck of mass $$M = 4000 kg is $$stopped at a light. A car of mass $$m = 1000 kg $$and speed $$v_i = 10 m/s $$hits it from behind. The truck and car stick together. What is their final speed?

Accepted Answer

$$2 m/s$$

Question 16

Two hikers, each of mass $$m$$, climb the same hill. The first hiker gets to the top in 1 hour, the second in 4 hours. The power expended by the first hiker is ______ as the second hiker.

Accepted Answer

4 times as much

Question 17

A car drives along a freeway with constant velocity. Which statement best describes the total work $$W_{	ext{TOT}}$$ done on the car by all forces as it moves?

Accepted Answer

$$W_{	ext{TOT}} = 0$$

Question 18

I throw a ball up in the air. During its motion, is the momentum of the ball conserved?

Accepted Answer

No

Question 19

You are driving your car in a circle of radius $$100 m$$, starting from rest and accelerating with constant angular acceleration $$\alpha. $$Halfway around the circle takes $$10$$ seconds. What is your speed at this point?

Accepted Answer

$$20 m/s$$

Question 20

A ballistic pendulum: a bullet of mass $$m is $$shot with speed $$v$$ into a block of mass $$M$$ hanging from a string of length $$L. $$The bullet sticks in the block and the block swings up to an angle $$	heta. $$What is the speed of the bullet?

Accepted Answer

$$\frac{m+M}{m} \sqrt{2gL(1-\cos	heta)}$$

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