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If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy?
A block with mass \( m \) slides at speed \( v_0 \) on a smooth surface and hits a stationary block with mass \( M \). They stick together and move at speed \( \frac{v_0}{3} \). Find \( M \) in terms of \( m \).
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?
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
A ball is launched and lands \( 20 \) \( \text{m} \) away below the launch point \( 2.5 \) \( \text{s} \) later. The maximum height reached is \( 8.0 \) \( \text{m} \). What was the original launch velocity?
Two students are on a balcony 19.6 m above the street. One student throws a ball vertically downward at 14.7 m/s. At the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down.
The coefficient of static friction between hard rubber and normal street pavement is about \(0.85\). On how steep a hill (maximum angle) can you leave a car parked?
A space probe far from the Earth is travelling at \( 14.8 \) \( \text{km s}^{-1} \). It has mass \( 1\,312 \) \( \text{kg} \). The probe fires its rockets to give a constant thrust of \( 156 \) \( \text{kN} \) for \( 220. \) \( \text{s} \). It accelerates in the same direction as its initial velocity. In this time it burns \( 150. \) \( \text{kg} \) of fuel.
Calculate the final speed of the space probe in \( \text{km s}^{-1} \).
A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( L \), then allowing the ball to move in a horizontal circle of radius \( R \).
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
A car accelerates from rest with an acceleration of \( 4.3 \, \text{m/s}^2 \) for a time of \( 6.8 \, \text{s} \). The car then slows to a stop with an acceleration of \( 5.1 \, \text{m/s}^2 \). What is the total distance traveled by the car?
A uniform, rigid rod of length \( 2 \) \( \text{m} \) lies on a horizontal surface. One end of the rod can pivot about an axis that is perpendicular to the rod and along the plane of the page. A \( 10 \) \( \text{N} \) force is applied to the rod at its midpoint at an angle of \( 37^{\circ} \). A second force \( F \) is applied to the free end of the rod so that the rod remains at rest, as shown in the figure. The magnitude of the torque produced by force \( F \) is most nearly
A pair of fuzzy dice is hanging by a string from your rearview mirror. You speed up from a stoplight. During the acceleration, the dice do not move vertically; the string makes an angle of \( 22^\circ \) with the vertical. The dice have a mass of \( 0.10 \, \text{kg} \). Determine the acceleration.
A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process?
A \(1509 \, \text{g}\) wood block is being pulled by the force meter at a constant velocity. Using the graph above, find:
The radius of the left piston is \( 0.12 \) \( \text{m} \) and the radius of the right piston is \( 0.65 \) \( \text{m} \). If \( f \) were raised by \( 14 \) \( \text{N} \), how much would \( F \) need to be increased to maintain equilibrium?
A centrifuge accelerates uniformly from rest to 15,000 rpm in 240 s. Through how many revolutions did it turn in this time?
A box of mass \(m\) is initially at rest at the top of a ramp that is at an angle \(\theta\) with the horizontal. The block is at a height \(h\) and length \(L\) from the bottom of the ramp. The coefficient of kinetic friction between the block and the ramp is \(\mu\). What is the kinetic energy of the box at the bottom of the ramp?
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.
A \(2 \, \text{kg}\) ball is swung in a vertical circle. The length of the string the ball is attached to is \(0.7 \, \text{m}\). It takes \(0.4 \, \text{s}\) for the ball to travel one revolution (assume the ball travels at constant speed).
Does the odometer of a car measure a scalar or a vector quantity? What about the speedometer?
A solid sphere of mass \( 1.5 \, \text{kg} \) and radius \( 15 \, \text{cm} \) rolls without slipping down a \( 35^\circ\) incline that is \( 7 \, \text{m} \) long. Assume it started from rest. The moment of inertia of a sphere is \( I= \frac{2}{5}MR^2 \).
A horizontal tube with two vertical T-branches (A and B) is partially submerged in a liquid, with the open ends of the branches exposed to the air. However, the section of the tube above point B is hidden from view and may either be wider or narrower than the section above A.
Air is blown through the horizontal tube, causing the liquid levels in the vertical branches to rise as shown. Based on the observed water levels, which of the following best describes the characteristics of the hidden section of the tube above B?
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