Question 1

A person stands on frictionless ice and throws a football forward, as shown in image 1. What happens to the person after the throw, and why?

Accepted Answer

The person moves backward due to conservation of momentum: $$m_{person} v_{person} = -m_{football} v_{football}.$$

Question 2

In image 2, a piano is held up by two cables at different angles. Which equation correctly represents the equilibrium of vertical forces?

Accepted Answer

$$T_1$$ \sin 60^\circ + $$T_2$$ \sin 45^\circ = F_G$$

Question 3

A mass hangs at rest from a spring as shown in image 3. Which statement is correct about the forces acting on the mass?

Accepted Answer

The upward spring force equals the downward gravitational force: $$F_s = F_G.$$

Question 4

In image 4, the spring is stretched by $$\Delta y. $$What is the correct expression for the spring force according to Hooke's Law?

Accepted Answer

$$F_{sp} = -k \Delta y$$

Question 5

A mass is attached to a spring and pulled downward, as in image 5. If the spring constant is $$k$$ and the displacement is $$\Delta y$$, what is the equilibrium condition?

Accepted Answer

$$k \Delta y = mg$$

Question 6

A piano is suspended by two cables as in image 2. If one cable breaks, what happens to the piano?

Accepted Answer

The piano will rotate and fall because the remaining cable cannot balance the torque and weight.

Question 7

If the person in image 1 throws a heavier object instead of a football with the same speed, what happens to the person's recoil velocity?

Accepted Answer

The recoil velocity increases because $$v_{person} = -\frac{m_{object} v_{object}}{m_{person}}.$$

Question 8

In image 3, if the spring is replaced with a stiffer one (larger $$k$$), what happens to the equilibrium position for the same mass?

Accepted Answer

The equilibrium position moves upward because $$\Delta y = \frac{mg}{k}$$ decreases.

Question 9

A mass is oscillating on a spring as in images 3–5. Which of the following best describes the net force when the mass is at its lowest point?

Accepted Answer

The net force is upward because the spring force exceeds gravity.

Question 10

A person on frictionless ice (image 1) catches a ball moving toward them. What happens to the person?

Accepted Answer

The person moves in the direction the ball was originally moving due to conservation of momentum.

Question 11

In image 2, if $$T_1 is $$increased while $$T_2$$ remains constant, what must happen to the angle of $$T_1 to $$keep the piano in equilibrium?

Accepted Answer

The angle must decrease to maintain vertical equilibrium.

Question 12

If the spring in image 4 is stretched twice as far, what happens to the spring force?

Accepted Answer

The spring force doubles: $$F_{sp} = -k (2\Delta y) = -2k\Delta y.$$

Question 13

A mass is attached to a spring and oscillates vertically. At what point is the acceleration of the mass zero?

Accepted Answer

At the equilibrium position where $$F_{sp} + F_G = 0.$$

Question 14

In image 2, what is the horizontal equilibrium condition for the piano?

Accepted Answer

$$T_1$$ \cos 60^\circ + $$T_2$$ \cos 45^\circ = 0$$

Newton's Laws, Equilibrium, and Spring Forces: Study Notes with Visual Examples

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