A \(5\)-meter long ladder is leaning against a wall, with the bottom of the ladder \(3\) meters from the wall. The ladder is uniform and has a mass of \(20 \, \text{kg}\). A person of mass \(80 \, \text{kg}\) is standing on the ladder at a distance of \(4\) meters from the bottom of the ladder. What is the force exerted by the wall on the ladder?
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?
In which of the following is the particle’s acceleration constant?
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 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 sample of an unknown material appears to weigh \( 285 \) \( \text{N} \) in air and \( 195 \) \( \text{N} \) when immersed in alcohol of specific gravity \( 0.700 \).
A rocket is sent to shoot down an invading spacecraft that is hovering at an altitude of \( 1500 \, \text{m} \). The rocket is launched with an initial velocity of \( 180 \, \text{m/s} \). Find the following:
An object weighs \( 300 \, \text{N} \) on Earth and \( 50 \, \text{N} \) on the Moon. Does the object have less inertia on the Moon?
Friction provides the force needed for a car to travel around a flat, circular race track. Answer the following:
Consider a solid uniform sphere of radius \(R\) and mass \(M\) rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?
An object is moving in a horizontal circle at a constant speed. Which of the following correctly describes the linear and angular velocities of the object between any point along the circular path?
A 2.0 kg wood box slides down a vertical wood wall while you push on it at a 45 ° angle. The coefficient of kinetic friction of wood µk = 0.200. What magnitude of force should you apply to cause the box to slide down at a constant speed?
When can the motion of a pendulum be modeled as simple harmonic motion?
If the coefficient of static friction is \( \mu_s = 0.5 \), how much force must be applied to a spring (spring constant of \( 0.8 \) \( \text{N/m} \)) which is attached to a block of wood (mass \( 4.0 \) \( \text{kg} \)) in order to just begin to move the block?
Which graph below shows that one of the runners started 10 meters further ahead of the other? Assume the y-axis is measured in meters and the x-axis is measured in seconds.
Two blocks of ice, one five times as heavy as the other, are at rest on a frozen lake. A person then pushes each block the same distance \(d\). Ignore friction and assume that an equal force \(F\) is exerted on each block. Which of the following statements is true about the kinetic energy of the heavier block after the push?
A rescue helicopter lifts a 79 kg person straight up by means of a cable. The person has an upward acceleration of 0.70 m/s2 and is lifted through a distance of 11 m.
A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard \( 3.4 \) \( \text{s} \) later. If the speed of sound is \( 340 \) \( \text{m/s} \), how high is the cliff?
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