Q: A 0.15 kg baseball is pitched at 20 m/s and hit back at 40 m/s in the opposite direction. What is the change in momentum of the ball?

$$\Delta p = 0.15 \times (40 + 20)$$

Question 1

A gymnast balances on a beam. For the gymnast to be in static equilibrium, which of the following must be true?

Accepted Answer

The net force and net torque on the gymnast must both be zero: $$\sum F_x = 0$$, $$\sum F_y = 0$$, $$\sum 	au = 0.$$

Question 2

A spring with spring constant $$k is $$stretched by a distance $$\Delta x. $$According to Hooke's Law, what is the force exerted by the spring?

Accepted Answer

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

Question 3

A tall bookshelf is placed upright on the floor. Which change will increase its stability against tipping?

Accepted Answer

Lowering its center of gravity or widening its base of support.

Question 4

A steel rod of length $$L$$ and cross-sectional area $$A is $$stretched by a force $$F. If $$the rod obeys Hooke's law, which equation relates the force to the change in length $$\Delta L$$ and Young's modulus $$Y$$?

Accepted Answer

$$F = Y \frac{A}{L} \Delta L$$

Question 5

During a collision, a soccer ball is kicked and the force on the ball varies with time. The impulse delivered to the ball is:

Accepted Answer

The area under the force vs. time curve: $$J = \int F(t) dt.$$

Question 6

A 0.15 kg baseball is pitched at 20 m/s and hit back at 40 m/s in the opposite direction. What is the change in momentum of the ball?

Accepted Answer

$$\Delta p = 0.15 	imes (40 + 20)$$

Question 7

Which statement best describes the impulse-momentum theorem?

Accepted Answer

Impulse delivered to an object equals the change in its momentum: $$J = \Delta p = m(v_f - v_i).$$

Question 8

A 1.0 kg box slides on a frictionless surface and collides with a 2.0 kg box, sticking together. If the initial speed of the 1.0 kg box is 2.0 m/s and the 2.0 kg box is at rest, what is their final speed after collision?

Accepted Answer

$$v_f = 0.67 m/s$$

Question 9

Two ice skaters, Sandra (45 kg) and David (80 kg), push off from each other on frictionless ice. If Sandra moves at 2.2 m/s after the push, what is David's speed?

Accepted Answer

$$v_D = 1.2 m/s$$

Question 10

A car crash safety feature, such as an airbag, reduces injury by:

Accepted Answer

Increasing the collision time, thereby reducing the average force: $$F_{avg} = \frac{\Delta p}{\Delta t}.$$

Question 11

Which of the following is true for the conservation of momentum in an isolated system?

Accepted Answer

The total momentum before an interaction equals the total momentum after: $$P_{i} = P_{f}.$$

Question 12

A 2-kg box and a 1-kg box are at rest on a frictionless surface. An explosion pushes them apart. If the 1-kg box moves at 4 m/s, what is the speed of the 2-kg box?

Accepted Answer

2 m/s in the opposite direction

Question 13

Which of the following best describes an explosion in terms of momentum?

Accepted Answer

Internal forces cause particles to move apart, but total momentum is conserved if the system is isolated.

Question 14

A tennis ball bounces off the ground. The force-time graph for the collision is triangular, with a maximum force $$F_{max}$$ and duration $$\Delta t. $$What is the impulse delivered to the ball?

Accepted Answer

$$J = \frac{1}{2} F_{max} \Delta t$$

Question 15

A moving car of mass $$m$$ and velocity $$v$$ comes to a stop in time $$\Delta t$$ due to a constant braking force. What is the magnitude of the average force required?

Accepted Answer

$$F_{avg} = \frac{mv}{\Delta t}$$

Question 16

In a perfectly inelastic collision, two objects stick together after colliding. Which statement is true?

Accepted Answer

Momentum is conserved, but kinetic energy is not.

Question 17

A 1.0 kg cue ball is struck by a cue stick, exerting a force for 0.01 s. If the average force is 200 N, what is the impulse delivered to the ball?

Accepted Answer

$$J = 2 kg-m/s$$

Question 18

A system consists of two particles with momenta $$p_1$$ and $$p_2. $$What is the total momentum of the system?

Accepted Answer

$$P = p_1$ + p_2$

Question 19

Which of the following is a correct application of the impulse approximation in collision problems?

Accepted Answer

Neglecting all forces except the impulsive force during the brief collision time.

Physics for Life Sciences I – Lecture 14: Static Equilibrium, Hooke’s Law, Stability, and Elastic Materials

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