Question 1

Which of Newton's laws explains why a passenger in a car feels pushed outward when the car rounds a curve at high speed?

Accepted Answer

Newton's 1st Law: Objects in motion remain in motion unless acted upon by a force.

Question 2

A 70 kg person jumps vertically, lowering their center of gravity by $$c = 0.6 m. If $$the average force exerted by their legs is twice their weight, what is the height $$H$$ they reach? Use $$g = 9.8 m/s$^2.$$

Accepted Answer

$$H = c = 0.6 m$$

Question 3

Which equation correctly expresses the period $$T of a $$simple pendulum of length $$l$$ for small angles?

Accepted Answer

$$T = 2\pi \sqrt{l/g}$$

Question 4

A car of weight $$W$$ moves on a flat curve of radius $$R. If $$the coefficient of friction between the tires and the road is $$\mu$$, what is the maximum speed $$v_{max}$$ before skidding occurs?

Accepted Answer

$$v_{max} = \sqrt{\mu g R}$$

Question 5

During a vertical jump, which force is responsible for accelerating the jumper upwards before leaving the ground?

Accepted Answer

The net upward force $$F - W$$

Question 6

If a simple pendulum is displaced and released, at which point is its kinetic energy maximized?

Accepted Answer

As it passes through the center position

Question 7

A runner leans towards the center of a curved track while running. What is the main reason for this?

Accepted Answer

To balance the centripetal force required to follow the curve

Question 8

What is the work done by the leg muscles in a single vertical jump for a 70 kg person jumping 0.6 m high? Use $$g = 9.8 m/s$^2.$$

Accepted Answer

$$411$$ Joules

Question 9

Which of the following best describes Newton's 3rd Law in the context of a vertical jump?

Accepted Answer

The force exerted by the jumper on the ground is matched by an equal and opposite force from the ground on the jumper.

Question 10

If the gravitational acceleration on the Moon is $$g_{moon} = g_{earth}/6$$, how high could a person jump on the Moon compared to Earth, assuming the same force and crouch distance?

Accepted Answer

Six times higher than on Earth

Question 11

A pendulum of length $$l is $$swinging with small amplitude. If the period is $$T$$, what happens to $$T if$$ $$l is $$quadrupled?

Accepted Answer

The period doubles

Question 12

Which formula gives the final velocity $$v of an $$object under constant acceleration $$a$$ after time $$t$$, starting from initial velocity $$v_0$$?

Accepted Answer

$$v = v_0$ + a t$$

Question 13

In the context of energy consumption during exercise, if a muscle has an efficiency of 20%, what fraction of the chemical energy consumed is converted to mechanical work?

Accepted Answer

One fifth

Question 14

A car of mass $$m is $$moving at speed $$v$$ around a curve of radius $$R. $$What is the expression for the required centripetal force?

Accepted Answer

$$F_c = m v^2$ / R$$

Question 15

Which statement about translational and rotational motion is correct?

Accepted Answer

In pure translational motion, all parts of the body have the same velocity and acceleration.

Question 16

During walking, the motion of the swinging foot can be modeled as:

Accepted Answer

Approximately a half-cycle of simple harmonic motion

Question 17

If a pendulum is at the extreme of its swing, what type of energy does it possess?

Accepted Answer

Entirely potential energy

Question 18

What is the maximum tangential acceleration $$a_{max} of a $$pendulum with amplitude $$A$$ and period $$T$$?

Accepted Answer

$$a_{max} = 4 \pi^2$ A / T^2$

Question 19

Which equation describes the height $$H$$ attained in a vertical jump, given force $$F$$, weight $$W$$, and crouch distance $$c$$?

Accepted Answer

$$H = (F - W) c / W$$

Foundations of Motion: Newton's Laws, Translational and Rotational Motion, and Applications

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