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A baseball, mass \(0.5 \, \text{kg}\), is traveling to the right at \(32.2 \, \text{m/s}\) when it is hit by a bat and travels the opposite direction at \(72.2 \, \text{m/s}\). The bat hits the ball with a force of \(1,222 \, \text{N}\). What is the ball’s change in momentum and how long was the ball in contact with the bat?
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?
A block starts at rest on a frictionless inclined track which then turns into a circular loop of radius \( R \) and is vertical. In terms of \( R \) and constants, find the minimum height \( h \) above the bottom of the loop the block must start from so it makes it around the loop.
A child (\(m = 32 \, \text{kg}\)) in a boat (\(m = 71 \, \text{kg}\)) throws a \(7.1 \, \text{kg}\) package out horizontally with a speed of \(12.2 \, \text{m/s}\). Calculate the velocity of the boat immediately after, assuming it was initially at rest. Ignore water resistance.
What is the weight of a person who has a mass of \(75 \, \text{kg}\)?
A box with a mass of \( M \) rests on a scale in an elevator that is moving downwards. The elevator slows with an acceleration of \( \dfrac{g}{4} \). Which of the following will give the reading of the scale?
The object shown in the diagram below consists of a cylinder of mass \( 100 \) \( \text{kg} \) and radius \( 25.0 \) \( \text{cm} \) connected by four thin rods, each of mass \( 5.00 \) \( \text{kg} \) and length \( 0.75 \) \( \text{m} \), to a thin-outer ring of mass \( 20.0 \) \( \text{kg} \). A small chunk of metal of mass \( 1.00 \) \( \text{kg} \) is welded to the outer ring. Determine the moment of inertia of the entire assembly about the center of the inner cylinder, treating the metal chunk as a point mass. Hint: The moment of inertia of a disk about it center is \(\tfrac{1}{2} M R^2\), a thin rod about it center is \(\tfrac{1}{12}ML^2\), and a thin hoop about its center is \(I = MR^2\).
The diagram above shows a marble rolling down an incline, the bottom part of which has been bent into a loop. The marble is released from point A at a height of \(0.80 \, \text{m}\) above the ground. Point B is the lowest point and point C the highest point of the loop. The diameter of the loop is \(0.35 \, \text{m}\). The mass of the marble is \(0.050 \, \text{kg}\). Friction forces and any gain in kinetic energy due to the rotating of the marble can be ignored. When answering the following questions, consider the marble when it is at point C.
Why do raindrops fall with constant speed during the later stages of their descent?
The total energy of a system in SHM is given by \( E \). At what displacement from equilibrium is the kinetic energy equal to the potential 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 \( m \).
The axle (the black dot) in Figure 1 is half the distance from the center to the rim. Suppose \( d = 30 \) \( \text{cm} \). What is the torque that the axle must apply to prevent the disk from rotating? Express your answer in newton-meters. Use positive value for the counterclockwise torque and negative value for the clockwise torque.
An arrow is shot horizontally from a distance of \( 20 \, \text{m} \) away. It lands \( 0.05 \, \text{m} \) below the center of the target. If air resistance is negligible, what was the initial speed of the arrow?
A pump, submerged at the bottom of a well that is \( 35 \) \( \text{m} \) deep, is used to pump water uphill to a house that is \( 50 \) \( \text{m} \) above the top of the well, as shown to the right. The density of water is \( 1000 \) \( \text{kg/m}^3 \). All pressures are gauge pressures. Neglect the effects of friction, turbulence, and viscosity.
Two objects, \( A \) and \( B \), move toward one another. Object \( A \) has twice the mass and half the speed of object \( B \). Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?
A fisherman is standing in the back of his small fishing boat (the mass of the fisherman is the same as the mass of the boat) and he is a few meters from shore. He is done fishing so he starts walking towards the shore so he can get off the boat. What happens to the boat and the fisherman? Select all that apply and assume there is no friction between the boat and the water.
Imagine a hypothetical planet that has two moons. Moon \(\#1\) is in a circular orbit of radius \(R\) and has a mass \(M\).
Three blocks of masses \(5 \, \text{kg}\), \(4 \, \text{kg}\), and \(3 \, \text{kg}\) are placed side by side in that order. A \(25 \, \text{N}\) force applied on the \(5 \, \text{kg}\) block accelerates all three blocks together to the right. Find the acceleration of the blocks and the normal force the \(4 \, \text{kg}\) block exerts on the \(3 \, \text{kg}\) block.
A clothesline is stretched between two trees. A tire hangs in the middle of the line, and the two halves of the line make equal angles with the horizontal. The tension in the line is
The moment of inertia of a solid cylinder about its axis is given by \( I = \frac{1}{2}mR^2 \). If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is
A crate is pulled 2.5 m at constant velocity along a 25° incline. The coefficient of kinetic friction between the crate and the plane is 0.250. What is the efficiency of this procedure?
A ski lift carries skiers along a \(695 \, \text{m}\) slope inclined at \(34^\circ\). To lift a single rider, it is necessary to move \(72 \, \text{kg}\) of mass to the top of the lift. Under maximum load conditions, five riders per minute arrive at the top. If \(65\%\) of the energy supplied by the motor goes to overcoming friction, what average power must the motor supply?
A solid ball and a cylinder roll down an inclined plane. Which reaches the bottom first?
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