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This exam was created by a large language model. Please use it with caution, as inaccuracies may be present. Always verify critical information.

Which of the following statements about displacement and distance is true?

Select one option

Displacement is always greater than or equal to distance.

Distance is a vector quantity, while displacement is a scalar quantity.

Displacement can be zero even if the distance traveled is non-zero.

Distance is the shortest path between two points, while displacement is the total path length.

A velocity-time graph shows a horizontal line above the t-axis. Which of the following describes the motion?

Select one option

The object is at rest.

The object is moving with constant negative acceleration.

The object is moving with constant positive velocity.

The object is moving with increasing speed.

An object starts from rest and accelerates uniformly at $2.0\, \text{m/s}^2$ for $5.0\, \text{s}$ . How far does it travel during this time?

Select one option

$10.0\, \text{m}$

$25.0\, \text{m}$

$50.0\, \text{m}$

$100.0\, \text{m}$

A projectile is launched horizontally from a height $h$ with an initial speed $v_0$ . Neglecting air resistance, what is the time it takes to reach the ground?

Select one option

$\\frac{v_0}{g}$

$\\frac{h}{v_0}$

$\\sqrt{\\frac{2h}{g}}$

$\\frac{v_0^2}{2g}$

A $5.0\, \text{kg}$ object is subjected to a net force of $20.0\, \text{N}$ . What is the acceleration of the object?

Select one option

$0.25\, \text{m/s}^2$

$4.0\, \text{m/s}^2$

$15.0\, \text{m/s}^2$

$100.0\, \text{m/s}^2$

When a swimmer pushes water backward, the water pushes the swimmer forward. This is an example of:

Select one option

Newton's First Law of Motion

Newton's Second Law of Motion

Newton's Third Law of Motion

The Law of Conservation of Momentum

Which of the following statements about friction is true?

Select one option

Static friction is always greater than kinetic friction.

Kinetic friction acts in the direction of motion.

The coefficient of kinetic friction is typically greater than the coefficient of static friction.

Friction always causes an object to slow down.

An object moves in a circular path at constant speed. Which of the following is true about its acceleration?

Select one option

Its acceleration is zero.

Its acceleration is constant in magnitude and direction.

Its acceleration is directed tangent to the path.

Its acceleration is directed towards the center of the circle.

Two blocks, $m_1$ and $m_2$ , are connected by a massless string over a frictionless pulley. If $m_1 > m_2$ , what is the direction of the net force on the system?

Select one option

Towards $m_1$

Towards $m_2$

Zero

Cannot be determined without knowing the exact masses.

10.

A $2.0\, \text{kg}$ object accelerates from rest to $4.0\, \text{m/s}$ . What is the net work done on the object?

Select one option

$4.0\, \text{J}$

$8.0\, \text{J}$

$16.0\, \text{J}$

$32.0\, \text{J}$

11.

A ball is dropped from a height $H$ . At what height above the ground will its kinetic energy be equal to its potential energy?

Select one option

$H/4$

$H/2$

$H/\\sqrt{2}$

Cannot be determined without knowing the mass of the ball.

12.

A constant force of $100\, \text{N}$ pushes a $20\, \text{kg}$ object over a distance of $5.0\, \text{m}$ in $2.0\, \text{s}$ . What is the average power delivered by the force?

Select one option

$250\, \text{W}$

$500\, \text{W}$

$1000\, \text{W}$

$2000\, \text{W}$

13.

A spring with a spring constant $k$ is stretched by a distance $x$ . What is the potential energy stored in the spring?

Select one option

$kx$

$k/x$

$\\frac{1}{2}kx^2$

$2kx^2$

14.

A block slides down a rough incline. Which of the following statements is true regarding the energy of the block-Earth system?

Select one option

Mechanical energy is conserved.

Kinetic energy is converted into potential energy.

Some mechanical energy is transformed into thermal energy.

The work done by friction increases the total mechanical energy.

15.

According to the First Law of Thermodynamics, if $500\, \text{J}$ of heat is added to a system and the system does $200\, \text{J}$ of work, what is the change in the internal energy of the system?

Select one option

$+700\, \text{J}$

$+300\, \text{J}$

$-300\, \text{J}$

$-700\, \text{J}$

16.

Which mode of heat transfer involves the movement of fluid?

Select one option

Conduction

Convection

Radiation

Advection

17.

An ideal gas is kept in a rigid container. If the temperature of the gas is doubled, what happens to its pressure?

Select one option

The pressure halves.

The pressure remains constant.

The pressure doubles.

The pressure quadruples.

18.

To melt $1.0\, \text{kg}$ of ice at $0^\circ\text{C}$ requires $3.34 \times 10^5\, \text{J}$ of heat. This value represents the:

Select one option

Specific heat capacity of ice

Latent heat of fusion of water

Latent heat of vaporization of water

Thermal conductivity of ice.

19.

A projectile is launched from the base of a ramp that makes an angle of $\theta = 30^\circ$ with the horizontal. The projectile is launched with an initial speed of $v_0 = 20.0\, \text{m/s}$ at an angle of $\alpha = 60^\circ$ above the horizontal. Assume the base of the ramp is at the origin $(0,0)$ . Neglect air resistance.

a. Derive an expression for the time $t$ at which the projectile strikes the ramp. b. Calculate the distance $D$ along the incline from the launch point to where the projectile strikes the ramp. c. What are the horizontal and vertical components of the projectile's velocity just before it strikes the ramp? d. At the peak of its trajectory, what is the magnitude and direction of the net force acting on the projectile? Explain your reasoning.

20.

A block of mass $m = 2.0\, \text{kg}$ is released from rest at the top of a ramp inclined at an angle of $\theta = 30^\circ$ to the horizontal. The block slides down the ramp, which has a length $L = 3.0\, \text{m}$ . The coefficient of kinetic friction between the block and the ramp is $\mu_k = 0.20$ . At the bottom of the ramp, the block encounters a horizontal spring with a spring constant $k = 400\, \text{N/m}$ .

a. Calculate the speed of the block just as it reaches the bottom of the ramp, before it contacts the spring. b. Determine the maximum compression $x_{max}$ of the spring. c. Calculate the total work done by friction as the block slides from the top of the ramp until the spring reaches its maximum compression. d. After the spring reaches maximum compression, it pushes the block back up the ramp. What is the minimum coefficient of static friction required for the block to remain at rest at the highest point it reaches on the ramp after being pushed back up, assuming it doesn't leave the spring?

21.

One mole of an ideal monatomic gas undergoes the cycle shown in the P-V diagram below. The cycle consists of three processes:

Process A $\to$ B: Isochoric (constant volume) heating.
Process B $\to$ C: Isothermal expansion.
Process C $\to$ A: Adiabatic compression.

Given: $P_A = 1.0 \times 10^5\, \text{Pa}$ $V_A = 1.0\, \text{m}^3$ $P_B = 3.0 \times 10^5\, \text{Pa}$ $V_B = 1.0\, \text{m}^3$ $V_C = 3.0\, \text{m}^3$ The gas is monatomic, so $\gamma = 5/3$ . ( $R = 8.31\, \text{J/(mol} \cdot \text{K)}$ ).

a. Sketch the P-V diagram for this cycle, clearly labeling points A, B, and C, and indicating the direction of each process. b. Calculate the work done ( $W$ ) by the gas for each process: A $\to$ B, B $\to$ C, and C $\to$ A. c. Calculate the heat ( $Q$ ) absorbed or released by the gas for each process: A $\to$ B, B $\to$ C, and C $\to$ A. d. Calculate the net change in internal energy ( $\Delta U_{net}$ ) for the entire cycle.

22.

Design an experiment to determine the coefficient of kinetic friction ( $\mu_k$ ) between a wooden block and a wooden surface. Your design should allow for quantitative measurement and analysis.

a. List the necessary equipment. b. Describe the procedure, including the measurements to be taken. c. Explain how the data would be analyzed to determine $\mu_k$ , including any relevant formulas or graphs. d. Identify potential sources of error in the experiment and suggest ways to minimize them.