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Intermediate
Proportional Analysis
MCQ

The exoplanet HD 69830b has a mass 10 times that of the Earth and a radius 5 times that of the Earth. The value of g on HD 69830b is most nearly

Intermediate
Mathematical
MCQ

A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger.

Students are provided with data in which an experiment was conducted to determine the relationship between the length of the pendulum and the period of oscillation. The data include a pendulum of length 0.5 m, for which it took 81 s for the pendulum bob to oscillate 10 times. However, the experiment was conducted at a location that is not near Earth’s surface. The gravitational field strength where the experiment was conducted is most nearly

Intermediate
Mathematical
MCQ

In the lab, a student is given a glass beaker filled with water with an ice cube of mass \( m \) and volume \( V_c \) floating in it.

The downward force of gravity on the ice cube has magnitude \( F_g \). The student pushes down on the ice cube with a force of magnitude \( F_P \) so that the cube is totally submerged. The water then exerts an upward buoyant force on the ice cube of magnitude \( F_B \). Which of the following is an expression for the magnitude of the acceleration of the ice cube when it is released?

Advanced
Proportional Analysis
FRQ

On a distant planet, golf is just as popular as it is on Earth. A golfer tees off and drives the ball \(3.5\) times as far as he would have on Earth, given the same initial velocities on both planets. The ball is launched at a speed of \(45 \, \text{m/s}\) at an angle of \(29^\circ\) above the horizontal. When the ball lands, it is at the same level as the tee. On the distant planet find:

Intermediate
Mathematical
GQ

A major-league pitcher can throw a baseball in excess of \( 41.0 \, \text{m/s} \). If a ball is thrown horizontally at this speed, how much will it drop by the time it reaches a catcher who is \( 17.0 \, \text{m} \) away from the point of release?

Advanced
Mathematical
FRQ

The graph above shows the angular velocity of a spinning wheel (radius = \( 25 \) \( \text{cm} \)) as a function of time.

Intermediate
Mathematical
GQ

A 84.4 kg climber is scaling the vertical wall. His safety rope is made of a material that behaves like a spring  that has a spring constant of 1.34 x 103 N/m. He accidentally slips and falls 0.627 m before the rope runs out of slack. How much is the rope stretched when it breaks his fall and momentarily brings him to rest?

Beginner
Proportional Analysis
MCQ

What is the effect on the period of a pendulum if you double its length?

Advanced
Mathematical
FRQ

A particle of mass \(m\) slides down a fixed, frictionless sphere of radius \(R\), starting from rest at the top.

In terms of \(m\), \(g\), \(R\), and \(\theta\), determine each of the following for the particle while it is sliding on the sphere.

Intermediate
Mathematical
GQ

A \(5.0 \, \text{g}\) coin is placed \(15 \, \text{cm}\) from the center of a turntable. The coin has coefficients of static and kinetic friction of \(\mu_s = 0.80\) and \(\mu_k = 0.50\). The turntable slowly speeds up to \(60 \, \text{rpm}\). Does the coin slide off the turntable?

Intermediate
Conceptual
MCQ

A constant force of strength \( 20 \) \( \text{N} \) acts on an object of mass \( 3 \) \( \text{kg} \) as it moves a distance of \( 4 \) \( \text{m} \). If this force is applied perpendicular to the \( 4 \) \( \text{m} \) displacement, the work done by the force is equal to:

Advanced
Conceptual
MCQ

A person holds a book at rest a few feet above a table. The person then lowers the book at a slow constant speed and places it on the table. Which of the following accurately describes the change in the total mechanical energy of the Earth–book system?

Intermediate
Mathematical
GQ

Astronaut Jennifer’s lifeline to her spaceship comes loose and she finds herself stranded, “floating” \( 100 \) \( \text{m} \) from the mothership. She suddenly throws her \( 2.00 \) \( \text{kg} \) wrench at \( 20 \) \( \text{m/s} \) in a direction away from the ship. If she and her spacesuit have a combined mass of \( 200 \) \( \text{kg} \), how long does it take her to coast back to her spaceship?

Intermediate
Mathematical
GQ

In a town’s water system, pressure gauges in still water at street level read \( 150 \) \( \text{kPa} \). If a pipeline connected to the system breaks and shoots water straight up, how high above the street does the water shoot?

Intermediate
Proportional Analysis
MCQ

A fluid flows through the two sections of cylindrical pipe shown in the figure. The narrow section of the pipe has radius \( R \) and the wide section has radius \( 2R \). What is the ratio of the fluid’s speed in the wide section of pipe to its speed in the narrow section of pipe, \( \dfrac{v_{\text{wide}}}{v_{\text{narrow}}} \)?

Intermediate
Proportional Analysis
GQ

The Earth’s radius is \(6.37 \times 10^{6} \, \text{m}\). What is the radius of a planet that has the same mass as Earth but on which the free-fall acceleration is \(5.50 \, \text{m/s}^2\)?

Intermediate
Mathematical
GQ

Mary and Sally are in a foot race. When Mary is \( 22 \) \( \text{m} \) from the finish line, she has a speed of \( 4.0 \) \( \text{m/s} \) and is \( 5.0 \) \( \text{m} \) behind Sally, who has a speed of \( 5.0 \) \( \text{m/s} \). Sally thinks she has an easy win and, during the remaining portion of the race, decelerates at a constant rate of \( 0.40 \) \( \text{m/s}^2 \) until she reaches the finish line. What constant acceleration must Mary maintain during the remaining portion of the race if she wishes to cross the finish line side-by-side with Sally?

Intermediate
Mathematical
MCQ
The diagram shows a horizontally oriented circular pipe of initial diameter labeled ( D ) that bends smoothly upward into an S-shape and then levels off into a horizontal section whose diameter is labeled ( 2D ). On the lower horizontal section, a point on the pipe’s centerline is marked with a solid black dot and labeled "A". A right-pointing horizontal arrow originates at point A and is labeled ( v_0 ), indicating the fluid velocity at that point. Directly above point A, a dashed horizontal reference line extends across the page. A second dashed horizontal line, parallel to the first, is drawn through a point on the upper horizontal pipe section. The vertical distance between the two dashed lines is marked by a vertical bracket with arrowheads at both ends and labeled ( H ). On the upper horizontal pipe section, a solid black dot on the centerline is labeled "B". A vertical bracket on the left side of the lower dashed line shows the pipe diameter at A labeled ( D ). A similar bracket on the right side of the upper dashed line shows the pipe diameter at B labeled ( 2D ). All pipe walls are drawn as thin parallel curves representing the interior and exterior surfaces.

Water of density \( \rho \) flows through the section of circular pipe shown in the figure. At Point A, where the diameter of the pipe is \( D \), the water has a pressure \( P_0 \) and velocity \( v_0 \). Point B is located a vertical distance \( H \) above Point A in a section of the pipe that has diameter \( 2D \).

Which of the following expressions is equal to the pressure of the water at Point B?

Advanced
Mathematical
GQ

An object of unknown mass is acted upon by multiple forces:

  • \(100 \, \text{N}\) to the right at \(20^\circ\)
  • \(400 \, \text{N}\) to the left at \(40^\circ\) below the horizontal
  • \(500 \, \text{N}\) to the right at \(10^\circ\) below the horizontal

The coefficients of friction are \(\mu_s = 0.6\) and \(\mu_k = 0.2\). Starting from rest, the object travels \(10 \, \text{m}\) in \(4.5 \, \text{s}\). What is the mass of the unknown object?

Advanced
Mathematical
GQ

Find the downward acceleration of an elevator, given that the ratio of a person’s stationary weight to their weight in the elevator is \(5:4\).

Intermediate
Mathematical
MCQ

A solid ball of mass \( M \) and radius \( R \) has rotational inertia \( \frac{2}{5} M R^{2} \) about its center. It rolls without slipping along a level surface at speed \( v \) just before it begins rolling up an inclined plane. Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?

Intermediate
Mathematical
GQ

A ball is thrown horizontally from the roof of a building \( 7.5 \) \( \text{m} \) tall and lands \( 9.5 \) \( \text{m} \) from the base. What was the ball’s initial speed?

Advanced
Proportional Analysis
GQ

A cardinal (Richmondena cardinalis) of mass \( 3.80 \times 10^{-2} \) \( \text{kg} \) and a baseball of mass \( 0.150 \) \( \text{kg} \) have the same kinetic energy. What is the ratio of the cardinal’s magnitude \( p_c \) of momentum to the magnitude \( p_b \) of the baseball’s momentum?

Intermediate
Mathematical
MCQ

In which of the following is the particle’s acceleration constant?

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