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A car accelerates uniformly from rest to a speed of $20 \, \text{m/s}$ in $5.0 \, \text{s}$ . What is the distance traveled by the car during this time?

Select one option

$25 \, \text{m}$

$50 \, \text{m}$

$75 \, \text{m}$

$100 \, \text{m}$

Which of the following statements about an object in projectile motion (neglecting air resistance) is true?

Select one option

Its horizontal velocity continuously increases.

Its vertical acceleration continuously increases.

Its horizontal acceleration is zero.

Its vertical velocity is constant.

A ball is thrown vertically upward with an initial speed of $15 \, \text{m/s}$ . Approximately how long does it take to reach its maximum height? (Assume $g = 9.8 \, \text{m/s}^2$ )

Select one option

$0.65 \, \text{s}$

$1.53 \, \text{s}$

$2.00 \, \text{s}$

$3.06 \, \text{s}$

Position-Time Graph

A position-time graph for an object is shown below. At which point is the object moving with the greatest positive velocity?

Select one option

A boat travels at $4.0 \, \text{m/s}$ relative to the water. The river flows downstream at $3.0 \, \text{m/s}$ relative to the bank. If the boat heads directly across the river, what is the magnitude of the boat's velocity relative to the bank?

Select one option

$1.0 \, \text{m/s}$

$3.0 \, \text{m/s}$

$5.0 \, \text{m/s}$

$7.0 \, \text{m/s}$

An object experiences a net force of zero. Which of the following statements must be true?

Select exactly 2 option(s)

The object is at rest.

The object is moving at a constant velocity.

The object has zero acceleration.

The object has zero kinetic energy.

A $5.0 \, \text{kg}$ block is pulled across a horizontal surface by a $30 \, \text{N}$ force at an angle of $30^{\circ}$ above the horizontal. If the coefficient of kinetic friction is $0.20$ , what is the magnitude of the acceleration of the block? (Assume $g = 9.8 \, \text{m/s}^2$ )

Select one option

$1.8 \, \text{m/s}^2$

$2.5 \, \text{m/s}^2$

$3.4 \, \text{m/s}^2$

$4.1 \, \text{m/s}^2$

According to Newton's Third Law, for every action force, there is an equal and opposite reaction force. Which of the following pairs of forces illustrates this law?

Select one option

The force of gravity on an object and the normal force exerted by a surface on the object.

The tension in a rope pulling a block and the frictional force opposing the motion of the block.

The force exerted by a bat on a ball and the force exerted by the ball on the bat.

The force of air resistance on a falling object and the force of gravity on the falling object.

A car goes around a circular track at a constant speed. Which of the following statements is true about the net force on the car?

Select one option

The net force is zero.

The net force is directed tangent to the circle.

The net force is directed inward, towards the center of the circle.

The net force is directed outward, away from the center of the circle.

10.

A satellite orbits Earth in a circular path. If the orbital radius is doubled, what happens to the gravitational force between the Earth and the satellite?

Select one option

It remains the same.

It becomes half as strong.

It becomes one-fourth as strong.

It becomes twice as strong.

11.

An object moves with constant velocity. Which of the following statements about the net work done on the object is true?

Select one option

The net work done is positive.

The net work done is negative.

The net work done is zero.

The net work done is equal to the change in its potential energy.

12.

A $2.0 \, \text{kg}$ object is lifted vertically upward at a constant speed of $0.50 \, \text{m/s}$ for $4.0 \, \text{s}$ . How much work is done by the lifting force? (Assume $g = 9.8 \, \text{m/s}^2$ )

Select one option

$9.8 \, \text{J}$

$19.6 \, \text{J}$

$39.2 \, \text{J}$

$49.0 \, \text{J}$

13.

A motor does $500 \, \text{J}$ of work in $10 \, \text{s}$ . What is the power output of the motor?

Select one option

$5.0 \, \text{W}$

$50 \, \text{W}$

$500 \, \text{W}$

$5000 \, \text{W}$

14.

A spring with a spring constant of $200 \, \text{N/m}$ is compressed by $0.10 \, \text{m}$ from its equilibrium position. What is the elastic potential energy stored in the spring?

Select one option

$1.0 \, \text{J}$

$2.0 \, \text{J}$

$10 \, \text{J}$

$20 \, \text{J}$

15.

A $0.50 \, \text{kg}$ ball is dropped from a height of $10 \, \text{m}$ . What is its speed just before it hits the ground? (Neglect air resistance and assume $g = 9.8 \, \text{m/s}^2$ )

Select one option

$9.9 \, \text{m/s}$

$14 \, \text{m/s}$

$19.8 \, \text{m/s}$

$49 \, \text{m/s}$

16.

Which of the following is an example of an inelastic collision?

Select one option

A billiard ball striking another billiard ball and both moving away.

A perfectly elastic ball bouncing off a wall.

Two cars colliding and sticking together.

A basketball bouncing off the ground.

17.

Which of the following describes the behavior of an ideal gas when its volume is kept constant and its temperature is increased?

Select one option

Its pressure decreases.

Its pressure increases.

Its pressure remains constant.

Its density decreases.

18.

How much heat is required to raise the temperature of $0.50 \, \text{kg}$ of water from $20^{\circ}\text{C}$ to $100^{\circ}\text{C}$ ? (Specific heat capacity of water = $4186 \, \text{J/kg}\cdot^{\circ}\text{C}$ )

Select one option

$83720 \, \text{J}$

$167440 \, \text{J}$

$209300 \, \text{J}$

$418600 \, \text{J}$

19.

Which of the following methods of heat transfer does NOT require a medium?

Select one option

Conduction

Convection

Radiation

Evaporation

20.

A container of ideal gas is at a pressure of $1.0 \times 10^5 \, \text{Pa}$ and a volume of $2.0 \, \text{m}^3$ . If the pressure is increased to $3.0 \times 10^5 \, \text{Pa}$ while the temperature is kept constant, what is the new volume of the gas?

Select one option

$0.67 \, \text{m}^3$

$1.0 \, \text{m}^3$

$2.0 \, \text{m}^3$

$6.0 \, \text{m}^3$

21.

What happens to the internal energy of an ideal gas when it undergoes an isothermal expansion?

Select one option

It increases.

It decreases.

It remains constant.

It depends on the specific gas.

22.

An astronaut drops a hammer and a feather on the Moon. Which statement best describes their fall?

Select one option

The hammer hits the ground first because it has more mass.

The feather hits the ground first because it has less air resistance.

They hit the ground at the same time because there is no air resistance.

They float indefinitely because there is no gravity on the Moon.

23.

A block is at rest on an inclined plane. Which of the following forces prevents it from sliding down?

Select one option

Kinetic friction

Static friction

Normal force

Applied force

24.

A conservative force is one for which the work done by the force is independent of the path taken. Which of the following is a conservative force?

Select one option

Friction

Air resistance

Tension

Gravity

25.

A block of mass $M$ is attached to a string and swung in a vertical circle of radius $R$ . At the very top of the circle, the tension in the string is $T$ . What is the speed of the block at this point?

Select one option

$\sqrt{Rg}$

$\sqrt{\frac{R(T - Mg)}{M}}$

$\sqrt{\frac{R(T + Mg)}{M}}$

$\sqrt{\frac{TR}{M}}$

Projectile Motion and Forces

A projectile of mass $m = 2.0 \, \text{kg}$ is launched from the ground with an initial speed $v_0 = 25 \, \text{m/s}$ at an angle $\theta = 37^{\circ}$ above the horizontal. Air resistance is negligible. Assume $g = 9.8 \, \text{m/s}^2$ .

26.

(a) Calculate the initial horizontal and vertical components of the projectile's velocity.

27.

(b) Determine the time it takes for the projectile to reach its maximum height.

28.

29.

(d) Sketch the free-body diagram of the projectile at the peak of its trajectory. Explain the forces acting on it at that instant.

Conservation of Energy with Friction

A block of mass $M = 3.0 \, \text{kg}$ is released from rest at the top of a ramp of height $H = 5.0 \, \text{m}$ . The ramp makes an angle of $30^{\circ}$ with the horizontal. The coefficient of kinetic friction between the block and the ramp is $\mu_k = 0.25$ . Assume $g = 9.8 \, \text{m/s}^2$ .

30.

(a) Calculate the length of the ramp.

31.

(b) Calculate the work done by friction as the block slides down the ramp.

32.

Universal Gravitation and Circular Motion

A satellite of mass $m = 1000 \, \text{kg}$ orbits a planet of mass $M_P = 5.0 \times 10^{24} \, \text{kg}$ in a circular orbit of radius $r = 7.0 \times 10^6 \, \text{m}$ . The universal gravitational constant is $G = 6.67 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2$ .

33.

(a) Derive an expression for the orbital speed of the satellite in terms of $G$ , $M_P$ , and $r$ . Show all steps.

34.

(b) Calculate the orbital speed of the satellite using the given values.

35.

Calorimetry and Phase Change

A $0.15 \, \text{kg}$ sample of unknown metal at $150^{\circ}\text{C}$ is placed into a calorimeter containing $0.20 \, \text{kg}$ of water at $20^{\circ}\text{C}$ . The final equilibrium temperature of the system is $28^{\circ}\text{C}$ . Assume the calorimeter has negligible heat capacity. The specific heat capacity of water is $c_w = 4186 \, \text{J/kg}\cdot^{\circ}\text{C}$ .

36.

(a) Calculate the heat gained by the water.

37.

(b) Determine the specific heat capacity of the unknown metal.

38.

(c) If $0.05 \, \text{kg}$ of ice at $0^{\circ}\text{C}$ were added to the initial water ( $0.20 \, \text{kg}$ at $20^{\circ}\text{C}$ ) instead of the metal, how much heat would be required to melt all the ice? (Latent heat of fusion of ice $L_f = 3.34 \times 10^5 \, \text{J/kg}$ )

39.

(d) Discuss qualitatively what would happen to the final equilibrium temperature of the system (water + ice) compared to the case with the metal. Explain your reasoning.

Investigation of a Spring-Mass System

A student conducts an experiment to investigate the relationship between the applied force and the extension of a spring, and then the oscillation of a mass attached to it. They collect the following data for the force vs. extension:\n\n| Applied Force (N) | Spring Extension (m) |\n|-------------------|----------------------|\n| 0.0 | 0.000 |\n| 1.0 | 0.025 |\n| 2.0 | 0.050 |\n| 3.0 | 0.075 |\n| 4.0 | 0.100 |\n\nLater, a $0.50 \, \text{kg}$ mass is attached to the same spring and allowed to oscillate vertically.

40.

(a) Plot the data for Applied Force vs. Spring Extension on a graph. Determine the spring constant of the spring from your graph.

41.

(b) Calculate the period of oscillation of the $0.50 \, \text{kg}$ mass attached to this spring.

42.