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Intermediate
Conceptual
MCQ

A point \( P \) is subjected to three simultaneous forces of magnitudes \( F_A > F_B > F_C \). Point \( P \) is in equilibrium. Which of the following statements is not always true about the magnitudes of the forces?

  1. \[ F_A = F_B + F_C \]
  2. \( F_A \leq F_B + F_C \)
  3. \( F_A > F_B – F_C \)
Beginner
Mathematical
GQ

What force is necessary to stretch an ideal spring with a spring constant of \( 120 \) \( \text{N/m} \) by \( 30 \) \( \text{cm} \)?

Intermediate
Mathematical
GQ

When a horizontal force of \( 4.5 \, \text{N} \) acts on a block on a resistance-free surface, it produces an acceleration of \( 2.5 \, \text{m/s}^2 \). Suppose a second \( 4.0 \, \text{kg} \) block is dropped onto the first. What is the magnitude of the acceleration of the combination if the same force continues to act? Assume that the second block does not slide on the first block.

Beginner
Mathematical
FRQ

Vector \( A \) is \( 44.0 \) units and \( 28.0^\circ \) above the \( +x \) axis, vector \( B \) is \( 26.5 \) units and \( 56.0^\circ \) above the \( -x \) axis, and vector \( C \) is \( 31.0 \) units along the \( -y \) axis. Determine the resultant (sum) of the three vectors.

Advanced
Mathematical
GQ

A \(2.2 \times 10^{21} \, \text{kg}\) moon orbits a distant planet in a circular orbit of radius \(1.5 \times 10^8 \, \text{m}\). It experiences a \(1.1 \times 10^{19} \, \text{N}\) gravitational pull from the planet. What is the moon’s orbital period in Earth days?

Advanced
Mathematical
FRQ

A box of mass \( 20 \) \( \text{kg} \) moves to the right on a horizontal frictionless surface with a speed of \( 4.0 \) \( \text{m/s} \). The box collides with and remains attached to one end of a spring of negligible mass whose other end is fixed to a wall. After the collision, the spring compresses a maximum distance of \( 0.50 \) \( \text{m} \), and the box then oscillates back and forth.

Intermediate
Mathematical
GQ

The large piston in a hydraulic lift has a radius of \( 250 \) \( \text{cm}^2 \). What force must be applied to the small piston with a radius of \( 25 \) \( \text{cm}^2 \) in order to raise a car of mass \( 1500 \) \( \text{kg} \)?

Intermediate
Conceptual
GQ

List at least 2 everyday forces that are not conservative, and explain why they aren’t.

Intermediate
Mathematical
GQ

A ball is kicked horizontally off a 20 m tall cliff at a speed of 11 m/s. What is the final velocity of the ball right before it hits the ground?

Advanced
Mathematical
FRQ

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at \( +13.0 \, \text{m/s}^2 \). At \( t_1 \), the rocket engine is shut down and the sled moves with constant velocity \( v \) until \( t_2 \). The total distance traveled by the sled is \( 5.30 \times 10^3 \, \text{m} \) and the total time is \( 90.0 \, \text{s} \).

Advanced
Mathematical
FRQ

An eagle is flying horizontally at \(6 \, \text{m/s}\) with a fish in its claws. It accidentally drops the fish.

Advanced
Proportional Analysis
MCQ

An object weighs \( 432 \) \( \text{N} \) on the surface of Earth. At a height of \( 3R_{\text{Earth}} \) above Earth’s surface, what is its weight?

Beginner
Mathematical
GQ

A mechanic pushes a \(2500 \, \text{kg}\) car from rest to a final speed \(v\) by doing \(5.0 \times 10^3 \, \text{J}\) of work on the car. Frictional effect between the car and the ground are negligible. What is the final speed of the car?

Intermediate
Mathematical
MCQ

A cart starts from rest and accelerates uniformly at \(4.0 \, \text{m/s}^2\) for \(5.0 \, \text{s}\). It next maintains the velocity it has reached for \(10 \, \text{s}\). Then it slows down at a steady rate of \(2.0 \, \text{m/s}^2\) for \(4.0 \, \text{s}\). What is the final speed of the car?

Intermediate
Mathematical
MCQ

A block of mass \( 4.0 \) \( \text{kg} \) rests on an inclined plane. The coefficient of static friction between the block and the plane \( \mu_s \) is \( 0.4 \). Which of the following gives the angle of inclination at which the block will start to slide?

Advanced
Mathematical
FRQ

A Venturi meter is a device used for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed \( v_2 \) through a horizontal section of pipe with a cross-sectional area \( A_2 = 542 \) \( \text{cm}^2 \). The gas has a density of \( 1.35 \) \( \text{kg/m}^3 \). The Venturi meter has a cross-sectional area of \( A_1 = 215 \) \( \text{cm}^2 \) and has been substituted for a section of the larger pipe. The pressure difference between the two sections \( P_2 – P_1 = 145 \) \( \text{Pa} \).

Intermediate
Mathematical
MCQ

An air mattress pump blows air above a beach ball at \( 8 \) \( \text{m/s} \). The air below the beach ball is moving at \( \approx 0 \) \( \text{m/s} \). Assuming the beach ball diameter is \( 0.1 \) \( \text{m} \), meaning the areas for the top \& bottom are each \( \approx 0.03 \) \( \text{m}^2 \), and the density of air is \( 1 \) \( \text{kg/m}^3 \), what is the lift force on the beach ball?

Advanced
Mathematical
MCQ

Block \(m_2\) is stacked on top of block \(m_1\). Block \(m_1\) is connected by a light cord to block \(m_3\), which is pulled along a frictionless surface with a force \(F\) as shown in the diagram above. Block \(m_1\) is accelerated at the same rate as block \(m_2\) because of the frictional forces between the two blocks. If all three blocks have the same mass \(m\), what is the minimum coefficient of static friction between block \(m_1\) and block \(m_2\)?

Intermediate
Mathematical
MCQ

An object is moving at constant velocity. Which of the following could be the free-body diagram representing the forces acting on the object?

Advanced
Mathematical
MCQ

Ball 1 is dropped from rest at time \( t = 0 \) from a tower of height \( h \). At the same instant, ball 2 is launched upward from the ground with the initial speed \( v_0 \). If air resistance is negligible, at what time \( t \) will the two balls pass each other?

Intermediate
Conceptual
GQ

A 100-pound rock and a 1-pound metal arrow pointed downwards are dropped from height \( h \). Assuming there is no air resistance, which one hits the ground first and why?

Intermediate
Mathematical
GQ

A cat chases a mouse across a \(1.0 \, \text{m}\) high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor \(2.2 \, \text{m}\) from the edge of the table. When the cat slid off the table, what was its speed?

Advanced
Mathematical
GQ

A projectile is launched at an angle of \( 30^{\circ} \) and hits a vertical wall \( 40 \) \( \text{m} \) away. After bouncing back horizontally, it lands \( 15 \) \( \text{m} \) behind the launch point. How high up on the wall did the projectile strike?

Intermediate
Mathematical
FRQ
A right-triangle ramp is drawn on the left side of a horizontal baseline. The ramp’s hypotenuse slopes downward from left to right at an angle labeled “θ0” between the hypotenuse and the rightward horizontal baseline. The horizontal run of the ramp (its base) is marked as length D, starting at x = –D on the leftmost top point of the ramp and ending at x = 0 at the foot of the ramp. From x = 0 to x = 4D, the baseline is a straight horizontal line representing the rough surface. Tick marks on the baseline indicate positions x = 0, D, 2D, 3D, and 4D. The inclined segment is frictionless; the horizontal segment is shaded or marked as rough. No block is explicitly drawn on the diagram.

A block is initially at rest on top of an inclined ramp that makes an angle \( \theta_0 \) with the horizontal. The distance measured along the base of the ramp is \( D \). After the block is released from rest, it slides down the frictionless ramp and then continues onto a rough horizontal surface until it finally comes to rest at the position \( x = 4D \) measured from the base of the ramp. The coefficient of kinetic friction between the block and the rough horizontal surface is \( \mu_k \).

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