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Advanced
Mathematical
GQ

Find the escape speed from a planet of mass \(6.89 \times 10^{25} \, \text{kg}\) and radius \(6.2 \times 10^{6} \, \text{m}\).

Intermediate
Mathematical
GQ

The efficiency of a pulley system is 55%. The
pulleys are used to raise a mass of 90.0 kg to a height of
5.60 m. What force is exerted on the rope of the pulley
system if the rope is pulled for 22 m in order to raise
the mass to the required height?

Beginner
Mathematical
GQ

Three blocks are stacked on top of one another. The top block has a mass of \( 4.6 \, \text{kg} \), the middle one has a mass of \( 1.2 \, \text{kg} \), and the bottom one has a mass of \( 3.7 \, \text{kg} \).
Identify and calculate any normal forces between the objects.

Advanced
Mathematical
GQ

Find the net gravitational force on a \(2.0 \, \text{kg}\) sphere midway between a \(4.0 \, \text{kg}\) sphere and a \(7.0 \, \text{kg}\) sphere that are \(1.2 \, \text{m}\) apart.

Advanced
Proportional Analysis
MCQ

two block with same KE moving across an identical rough surface

Two blocks, \( m_2 > m_1 \), having the same kinetic energy, move from a frictionless surface onto a surface having friction coefficient \( \mu_k \). Which block will travel further before stopping.

Advanced
Mathematical
FRQ

On a frictionless horizontal air table, puck A (with mass \( 0.249 \) \( \text{kg} \)) is moving toward puck B (with mass \( 0.375 \) \( \text{kg} \)), which is initially at rest. After the collision, puck A has velocity \( 0.115 \) \( \text{m/s} \) to the left, and puck B has velocity \( 0.645 \) \( \text{m/s} \) to the right.

Advanced
Mathematical
MCQ
Wagon Wheel Structure Moment of Inertia Wheel Mass Wheel Radius
Wagon \(A\) Solid disk \[\frac{1}{2} M R^2\] \[ 0.5 \, \text{kg} \] \[ 0.1 \, \text{m} \]
Wagon \(B\) Solid disk \[\frac{1}{2} M R^2\] \[ 0.2 \, \text{kg} \] \[ 0.1 \, \text{m} \]
Wagon \(C\) Hollow hoop \[M R^2\] \[ 0.1 \, \text{kg} \] \[ 0.1 \, \text{m} \]

Three wagons have identical total mass (including their wheels) and each has four wheels. However, the wheels on each wagon have different designs with varying mass distributions and radii as shown in a reference chart. When accelerating each wagon from a standstill to \( 10 \) \( \text{m/s} \), which wagon requires the most energy input?

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 \( 1500 \) \( \text{kg} \)?

Beginner
Conceptual
MCQ

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?

Beginner
Mathematical
MCQ

Old-fashioned clocks and watches have an hour hand, a minute hand and a second hand. What is the angular frequency of the second hand?

Beginner
Conceptual
MCQ

An object can move upward while having a downward acceleration.

Intermediate
Mathematical
FRQ

On Earth, a simple pendulum of length \(1.2 \, \text{meters}\), mass of \(3 \, \text{kg}\), and amplitude of \(10\) degrees oscillates back and forth. Calculate:

Beginner
Mathematical
GQ

A person stands on a scale in an elevator. If the scale reads \( 600 \, \text{N} \) when that person is riding upward at a constant velocity of \( 4 \, \text{m/s} \), what is the scale reading when the elevator is at rest? Hint: The reading on the scale is simply the normal force.

Intermediate
Mathematical
GQ

There are two cables that lift an elevator, each with a force of \(10{,}000 \, \text{N}\). The \(1{,}000 \, \text{kg}\) elevator is lifted from the first floor and accelerates over \(10 \, \text{m}\) until it reaches its top speed of \(6 \, \text{m/s}\). What is the mass of the people in the elevator?

Advanced
Conceptual
MCQ

A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disk?

Intermediate
Conceptual
GQ

A stone hangs by a fine thread from the ceiling, and a section of the same thread dangles from the bottom of the stone. If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull?

Intermediate
Conceptual
MCQ

Two objects labeled K and L have equal mass but densities \( 0.95D_o \) and \( D_o \), respectively. Each of these objects floats after being thrown into a deep swimming pool. Which is true about the buoyant forces acting on these objects?

Beginner
Conceptual
FRQ

Intermediate
Mathematical
MCQ

Consider a solid uniform sphere of radius \(R\) and mass \(M\) rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Intermediate
Mathematical
FRQ

A train consists of \(50\) cars, each of which has a mass of \(6.1 \times 10^{3} \, \text{kg}\). The train has an acceleration of \(8.0 \times 10^{-2} \, \text{m/s}^2\). Ignore friction and determine the tension in the coupling at the following places:

Intermediate
Mathematical
FRQ

A sample of an unknown material appears to weigh \( 285 \) \( \text{N} \) in air and \( 195 \) \( \text{N} \) when immersed in alcohol of specific gravity \( 0.700 \).

Advanced
Mathematical
GQ

Block 2 initially is at rest. Block 1 travels towards block 2 and collides with Block 2 as shown above. Find the final velocities of both blocks assuming the collision is elastic.

Intermediate
Proportional Analysis
MCQ

A \( 60 \ \text{kg} \) person is riding in an elevator. At time \( t_1 \), the elevator is accelerating downward with a magnitude of \( 2 \ \text{m/s}^2 \). A short time later, at time \( t_2 \), the elevator is accelerating upward with a magnitude of \( 2 \ \text{m/s}^2 \). The ratio of the normal force exerted by the elevator on the person at time \( t_1 \) to that at time \( t_2 \) is most nearly

Beginner
Mathematical
MCQ

A box is sliding down an incline at a constant speed of \( 2 \) \( \text{m s}^{-1} \). The angle of the incline is \( \theta \). The magnitude of the total of the opposing forces is \( 16 \) \( \text{N} \). What is the force of gravity acting on the box?

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