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 file “EnergyCons” from the 1C03 lab folder on the desktop.

The file will expect your wireless force sensor to be connected. First turn on the force sensor (attached to the spring) by holding down the power button until a light appears. In the ‘Hardware Setup’ tab in Capstone should appear options to connect wireless devices. You will need to select YOUR sensor with the matching six digit identification code written on top of the force sensor.

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 (variable quantity and value) 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 ([latex]x[/latex]), 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 ([latex]x[/latex]), which describes the gravitational potential energy of the weight? How can you relate the height of the hanging mass, [latex]h[/latex] to the measured coordinate [latex]x[/latex]. (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?