Question

Video text description for the Direct Measurement Video of Dry-Ice Levitated Puck on a Ramp

In this video, a puck made out of dry ice is at the top of a ramp. At the bottom of the ramp is a spring, aligned parallel with the ramp. A scale marked off in centimeters overlays the video, also aligned parallel with the ramp, and a protractor indicates that the angle of the ramp is approximately 22 degrees. The video is recorded at 240 frames per second, resulting in playback motion 8 times slower than normal. A frame counter indicates the current frame. An action figure of Einstein looks on at the action.

At the start of the video, the puck is held in place by a strap. The left edge of the puck is at 0 centimeters and the right edge is at 7.7 centimeters. The height of the puck is approximately 2.6 centimeters.

At frame 82, the strap is released and the puck starts accelerating down the ramp. At frame 172, the left edge of the puck is at 25.3 centimeters. At this frame, the puck hits the spring, which then compresses as the puck continues to move down the ramp. At frame 184, the spring appears to be at its maximum compression and the puck is momentarily at rest. The left edge of the puck at this frame is at 29.7 centimeters.

As the video continues to play, the puck reverses direction as the spring uncompresses and bounces the puck back up the ramp, spinning a little while it slides. It does not slide all the way back to the top of the ramp, but instead at frame 274 the left edge of the puck gets only to about 4 centimeters on the scale. The puck then reverses direction one more time and slides back down the ramp, spinning as it slides, until the video stops.

PART G)Find the force constant of the spring. Assume that the angle that the ramp makes with the horizontal is 22∘. Recall that the mass of the puck is 0.180kg and g=9.80m/s2.

Hint 1. Finding the change in GPEopened hint

Remember that the GPE keeps decreasing as the spring is getting compressed. What is the overall displacement along the ramp from the initial moment?

Hint 2. Finding the maximum compression of the springopened hint

You can determine the maximum compression of the spring by carefully using the frame-by-frame advance.

Delta GPE = 0.167J By the way.

Answer 1

G) Compression in the spring x = 29.7-25.3 =4.4 cm

mass of the puck =0.180 kg

Let force constant be k . given angle of inclination =22

Velocity of the puck after 90 frames =90/240 seconds =(3/8)seconds is V =U+ at

U =0 a =gsin    t =3/8

V = 9.8 (sin22)(3/8) = 1.376 m/s

   Chane in kinetic energy of the puck is equal to change in potential energy of the spring

   0.5 mV^2 =0..5 kx^2

   mV^2 =kx^2

k = mV^2 /x^2 = 0.180(1.376)² /0.044²

   k = 176.03 N/m