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St. Louis Braid Company is a company “dedicated to the design, manufacture, and commercialization of braided and twisted threads, laces, shoelaces, strings, elastic, and technical threads.” St. Louis Braid sells to footwear manufacturers such as Nike and Merrell. Thus, as customers buy more shoes from those brands, sales of St. Louis Braid’s laces also increase. We refer to this connected activity as:

A small collar is attached to a spring and slides without friction along a circular rod in a vertical plane. The spring has an undeformed length of  and a spring constant of .  What is the potential energy stored in the spring when the collar is at point B?  Hint: convert inches to feet for consistent units! 

A ball is dropped from a boat so that its velocity when it strikes the surface of the water is . While in the water, the ball experiences an acceleration of

A person rides a bicycle on a track consists of two circular sections ABC and CDE joined smoothly as shown in the figure below. Both paths have a radius of

A rigid bar is supported on a fixed semicircular surface of radius and the ground as shown in the figure. If end A of the bar is moving with a speed of along the ground, what is the magnitude of the angular velocity of the bar,

A model rocket has been launched upwards from the ground at time and its velocity at any instant of time after is given by

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?