Author: Anonymous

A small slider C of weight can move in the slotted bar AB without friction as shown in the figure. The slider is attached to a spring of constant , which is unstretched at . The bar rotates at a constant angular speed of

A bucket full of ore is suspended from a traveling crane that moves along a stationary bridge. The crane is travelling at a speed of when it is brought to a sudden stop.  To what angle from the vertical would the bucket swing to before coming to an instantaneous stop?  Use . Enter a number correct to 2 decimal places with the angle specified in degrees.The answer will be between 20 degrees and 30 degrees.

A homogeneous sphere S, a uniform cylinder C, and a thin pipe P are in contact when they are released from rest on the inclined plane as shown in the figure below. All of the objects have the same mass . All three objects roll without slipping.  Use . What is the acceleration of the center of mass of the uniform cylinder C? 

A printer head, represented by the red square on the figure below, follows a path in Cartesian space described by the equation .  When , the horizontal components of velocity and acceleration of the printer head are and respectively. What are the vertical components of its velocity and acceleration?

An overhead garage door is guided by wheels at A and B that roll in horizontal and vertical tracks as shown in the figure below. When the angle

In the gear system shown below, gear A is fixed (no motion), and the bar AB connecting the centers of the two gears rotates with an angular velocity of

Consider the 2D motion of a rocket of mass in an elliptical orbit around the Earth. The attractive force that the Earth induces on the rocket is directed towards the center of the Earth and has a magnitude of where is the radius of the Earth, is the distance of the rocket from the center of the Earth, and is the acceleration due to gravity on the surface of the Earth.  Choose the correct equations of motion of the rocket. Mark all answers that are correct.

Two rotating rods are connected through a slider block D. At the instant shown, the rod attached at B rotates with an angular velocity

An airplane is used to drop water on brushfires. It is flying horizontally in a straight line with a velocity of  and at an altitude of above the ground.  Determine the distance at which the pilot should release the water so that it will hit the fire at B.  Use .

A uniform slender bar of length is initially vertical and at rest. Its upper end A is attached to a small roller constrained to move along a smooth horizontal surface (i.e., no friction). A horizontal force of  is suddenly applied to the roller as shown. Neglect the mass and size of the roller.  What is the angular acceleration of the bar immediately after the force is applied?