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A 0.28 kg puck is released from rest at the top of a 3.0 m high ramp. It slides

ID: 1704129 • Letter: A

Question

A 0.28 kg puck is released from rest at the top of a 3.0 m high ramp. It slides down the frictionless ramp and slides 1.5 m across a horizontal surface until hitting a 0.15 kg puck at rest. The two pucks stick together and continue sliding. They then encounter a spring with a spring constant of 262 N/m.
a) What was the initial gravitational potential energy of the puck?
b) What was the velocity of the puck as it reached the horizontal surface?
c) What was velocity of the two pucks after the collision?
d) How far is the spring compressed?




Explanation / Answer

The mass of the first puck m1 = 0.28kg

the height of the ramp h = 3.0m

the mass of the second puck m2 = 0.15kg

The spring constant k = 262 N/m

(a) The initial gravitational energy

              E = mgh = (0.28)(9.8)(3)

                          = 8.23 J

(b) from law of conservation of energy

              mgh = 1/2mv^2

then the velocity of the puck

               v = 2gh

                  = 2*9.8*3 = 7.67 m/s

(c) from law of conservation of momentum

           m1v1 = (m1 + m2) vf

therefore the velocity

         vf = m1v1/(m1+m2)

              = (0.28)(7.67) / (0.28+0.15)

              = 4.99 or 5m/s

(d) Again from law of conservation of energy

       1/2 (m1+ m2) vf^2 = 1/2 kx^2

       Therefore the compression

             x = [(m1+m2)/k ] vf

                = [(0.28+0.15)/262 ] (5)

                = 0.20m or 20cm