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A 0.4 kg object is attached to a horizontal spring undergoes SHM with the total energy of 0.2 J. The potential energy as a function of position presented by the graph.
A rocket explodes into two fragments, one \(25\) times heavier than the other. The change in momentum of the lighter fragment is
The alarm at a fire station rings and a 79.34-kg fireman, starting from rest, slides down a pole to the floor below (a distance of 4.20 m). Just before landing, his speed is 1.36 m/s. What is the magnitude of the kinetic frictional force exerted on the fireman as he slides down the pole?
Which of the following must be zero if an object is spinning at a constant rate? There may be more than one right answer.
A uniform copper disk of radius \( R \) has a moment of inertia \( I \) around an axis passing through the center of the disk perpendicular to its plane. If the radius of the disk were only \( \dfrac{R}{2} \), but the thickness were the same, what would be the moment of inertia in terms of \( I \)? Hint: The moment of inertia of a solid disk about its center is \(\frac{1}{2} M R^{2}\).
A stone is thrown vertically upward with a speed of \( 24.0 \) \( \text{m/s} \).
A child of mass \( 3 \) \( \text{kg} \) rotates on a platform of \( 10 \) \( \text{kg} \). They start walking towards the center while the platform is rotating. Which of the following could possibly decrease the total angular momentum of the child-platform system?
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.
Initially, a ball has an angular velocity of \( 5.0 \) \( \text{rad/s} \) counterclockwise. Some time later, after rotating through a total angle of \( 5.5 \) \( \text{radians} \), the ball has an angular velocity of \( 1.5 \) \( \text{rad/s} \) clockwise.
A uniform rope of weight \( 30 \, \text{N} \) hangs from a hook. A box of mass \( 40 \, \text{kg} \) is suspended from the rope. What is the tension in the rope?
Which statements are not valid for a projectile? Take up as positive.
Three forces of equal magnitude are applied to a \( 3 \)-m by \( 2 \)-m rectangle. Force \( F_1 \) and \( F_2 \) act at \( 45^\circ \) angles to the vertical as shown, while \( F_3 \) acts horizontally.
The displacement \( x \) of an object moving in one dimension is shown above as a function of time \( t \). The acceleration of this object must be
| Speed | \( 10 \, \mathrm{m/s} \) | \( 20 \, \mathrm{m/s} \) | \( 30 \, \mathrm{m/s} \) |
| Braking Distance | \( 6.1 \, \mathrm{m} \) | \( 23.9 \, \mathrm{m} \) | \( 53.5 \, \mathrm{m} \) |
A car of mass \( 1500 \, \mathrm{kg} \) is traveling at one of the speeds listed when the brakes are first applied. Using the data above, what is the magnitude of the average braking force required to stop the car?
The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that a leg bone of a healthy, \( 80 \) \( \text{kg} \) human can absorb about \( 240 \) \( \text{J} \). From what maximum height could a \( 80 \) \( \text{kg} \) person jump and land rigidly upright on both feet without breaking their legs? Assume that all energy is absorbed by the leg bones in a rigid landing. Express your answer with the appropriate units.
A cube of unknown material and uniform density floats in a container of water with \(60\%\) of its volume submerged. If this same cube were placed in a container of oil with density \(800\) \(\text{kg/m}^3\), what portion of the cube’s volume would be submerged while floating?
A \(10 \, \text{meter}\) long pendulum on the earth, is set into motion by releasing it from a maximum angle of less than \(10^\circ\) relative to the vertical. At what time \(t\) will the pendulum have fallen to a perfectly vertical orientation?
In the laboratory, you are given a cylindrical beaker containing a fluid and you are asked to determine the density \( \rho \) of the fluid. You are to use a spring of negligible mass and unknown spring constant \( k \) that is attached to a vertical stand.
A projectile is launched at an angle of \( 30^{\circ} \) and hits a vertical wall \( 40 \) \( \text{m} \) away. After bouncing back horizontally, it lands \( 15 \) \( \text{m} \) behind the launch point. How high up on the wall did the projectile strike?
An object at rest suddenly explodes into two fragments (\(m_1\) and \(m_2\)) by an explosion. Fragment \(m_1\) acquires \(3\) times the kinetic energy of the other. What is the ratio of \(m_1\) to \(m_2\)?
Consider a rigid body that is rotating. Which of the following is an accurate statement?
An airplane accelerates down a runway at \( 10 \, \text{m/s}^2 \). It reaches a final velocity of \( 200 \, \text{m/s} \) until it finally lifts off the ground. Determine the distance traveled before takeoff.
A space probe far from the Earth is traveling at 14.8 km/s. It has mass 1312 kg. The probe fires its rockets to give a constant thrust of 156 kN for 220 seconds. It accelerates in the same direction as its initial velocity. In this time it burns 150 kg of fuel. Calculate final speed of the space probe in km/s.
Note: This is a bonus question. Skip if you haven’t yet taken calculus.
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