Cons. of Energy Exercise 2

In this experiment, the motion of the cart will be monitored by a rotary motion sensor. (As the cart moves, the pulley rotates. An optical sensor in the pulley housing measures through what angle the pulley rotates. One complete rotation corresponds to a linear displacement equal to the circumference of the disc. The Capstone software does the conversion from the angular to the linear measure for you.)

Open the Capstone software.

a) Determine the reference frame used by the rotary motion sensor. (How does it assign the origin? Which direction defines the positive axis? How does this look for the 100 g weight?)

Move the cart as near to the force sensor as the barriers allow, so that the spring is at its natural length (i.e. it isn’t stretched or compressed). We will call this the initial configuration of the system.

b)  If you start the run with the system in this configuration, what coordinate will the rotary motion sensor assign to the position of the cart or weight?

c)  What is the spring’s elastic potential energy in this configuration? Given the sensor’s choice of reference frame, how would you write an equation, in terms of the measured coordinate, which describes the potential energy of the spring as a function of position?

d)  Given the sensor’s choice of reference frame, how would you write an equation, in terms of the measured coordinate, which describes the gravitational potential energy of the weight? (Check that your equation is consistent with the fact that the weight will lose gravitational potential energy as it falls.) What then is the initial gravitational potential energy?

e)  If the cart is released from rest at this position, what is the initial total mechanical energy of the system? Does this seem reasonable?