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On a strange, airless planet, a ball is thrown downward from a height of \( 17 \, \text{m} \). The ball initially travels at \( 15 \, \text{m/s} \). If the ball hits the ground in \( 1 \, \text{s} \), what is this planet’s gravitational acceleration?
Determine the distance from the Earth’s center to a point outside the Earth where the gravitational acceleration due to the Earth is \( \dfrac{1}{10} \) of its value at the Earth’s surface.
Find the tension in each cable supporting the gymnast who weighs \( 600 \) \( \text{N} \). The gymnast is at rest, holding a junction point where two cables are attached: one cable is horizontal, and the second cable is attached to the ceiling making an angle of \( 37^{\circ} \) above the horizontal, as shown in the diagram.
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?
A block with a mass of \( 4 \) \( \text{kg} \) is attached to a spring on the wall that oscillates back and forth with a frequency of \( 4 \) \( \text{Hz} \) and an amplitude of \( 3 \) \( \text{m} \). What would the frequency be if the block were replaced by one with one‑fourth the mass and the amplitude of the block is increased to \( 9 \) \( \text{m} \)?
A rod is initially at rest on a rough horizontal surface. Three forces are exerted on the rod with the magnitudes and directions shown in the figure. The force exerted in the center of the rod is an equidistant 0.5 m from both ends of the rod. If friction between the rod and the table prevents the rod from rotating, what is the magnitude of the torque exerted on the rod about its center from frictional forces?
A \( 4700 \, \text{kg} \) truck carrying a \( 900 \, \text{kg} \) crate is traveling at \( 25 \, \text{m/s} \) to the right along a straight, level highway, as shown above. The truck driver then applies the brakes, and as it slows down, the truck travels \( 55 \, \text{m} \) in the next \( 3.0 \, \text{s} \). The crate does not slide on the back of the truck.
In lacrosse, a typical throw is made by rotating the stick through an angle of roughly \(90^\circ\), then releasing the ball when the stick is vertical, as shown above. If the \(1 \, \text{meter}\) long stick is at rest when horizontal and the ball leaves the stick with a velocity of \(10 \, \text{m/s}\), what angular acceleration must the stick experience?
A golfer hits her ball in a high arcing shot. Air resistance is negligible. When the ball is at its highest point, which of the following is true?
A car is moving up the side of a circular roller coaster loop of radius \( 12 \) \( \text{m} \). The angular velocity is \( 1.8 \) \( \text{rad/s} \) and angular acceleration is \( -0.82 \) \( \text{rad/s}^2 \). The car is at the same elevation as the center of the loop. Find the magnitude and direction (relative to the horizontal) of the acceleration.
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?
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.
In a demonstration, a teacher holds the axle of a wheel that is spinning with constant angular speed. The teacher then releases the axle and the wheel begins to fall toward the ground. As the wheel falls, its angular speed remains constant. Which of the following correctly describes how the rotational kinetic energy \( K_{\text{rot}} \) of the wheel and the total kinetic energy \( K_{\text{tot}} \) of the wheel change, if at all, after the wheel is released but before it reaches the ground?
| \( K_{\text{rot}} \) | \( K_{\text{tot}} \) | |
|---|---|---|
| A | Constant | Constant |
| B | Constant | Increasing |
| C | Increasing | Constant |
| D | Increasing | Increasing |
A linear spring of negligible mass requires a force of \( 18.0 \, \text{N} \) to cause its length to increase by \( 1.0 \, \text{cm} \). A sphere of mass \( 75.0 \, \text{g} \) is then attached to one end of the spring. The distance between the center of the sphere \( M \) and the other end \( P \) of the un-stretched spring is \( 25.0 \, \text{cm} \). Then the sphere begins rotating at constant speed in a horizontal circle around the center \( P \). The distance \( P \) and \( M \) increases to \( 26.5 \, \text{cm} \).
A ball is kicked at a speed of \( v_0 \) at an angle \( \theta \) above the horizontal. The ball travels 25 meters horizontally. If the ball is kicked at \( 2v_0 \), what will the horizontal displacement be?
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.
Two disks, A and B, each experience a net external torque that varies over an interval of \( 5 \) \( \text{s} \). Disk B has a rotational inertia that is twice that of Disk A. The graph shown represents the angular momentum of the two disks as functions of time between \( t = 0 \) \( \text{s} \) and \( t = 5 \) \( \text{s} \). The average magnitudes of the net torques exerted on disks A and B from \( t = 0 \) \( \text{s} \) to \( t = 5 \) \( \text{s} \) are \( \tau_A \) and \( \tau_B \), respectively. Which of the following expressions correctly relates the magnitudes of the average torques?
What is the rotational inertia \( I \) of a disk with a radius \( R = 4 \) \( \text{m} \) and a mass \( 2 \) \( \text{kg} \)? The same disk is rotated around an axis that is \( 0.5 \) \( \text{m} \) from the center of the disk. What is the new rotational inertia \( I \) of the disk? What would the rotational inertia be if the disk axis was \( 3.75 \) \( \text{m} \) from the center?
An elevator carrying a person of mass \( m \) is moving upward and slowing down. How does the magnitude \( F \) of the force exerted on the person by the elevator floor compare with the magnitude \( mg \) of the gravitational force?
A car rounds a curve at a steady \( 50 \) \( \text{km/h} \). If it rounds the same curve at a steady \( 70 \) \( \text{km/h} \), will its acceleration be any different?
A plane, 220 meters high, is dropping a supply crate to an island below. It is traveling with a horizontal velocity of 150 m/s. At what horizontal distance must the plane drop the supply crate for it to land on the island? Use \( g = 9.81 \, m/s^2\).
The diagram above shows a hydraulic chamber with a spring \( (k_s = 1250 \, \text{N/m}) \) attached to the input piston and a rock of mass \( 55.2 \, \text{kg} \) resting on the output plunger. The input piston and output plunger are at about the same height, and each has negligible mass. The chamber is filled with water.
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?
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