Question

A block (6 kg) starts from rest and slides down a frictionless ramp #1 of height 6 m. The block then slides a horizontal distance of 1 m on a rough surface with kinetic coefficient of friction μk = 0.5. Next, it slides back up another frictionless ramp #2. Find the following numerical energy values: 1.Initial gravitational potential energy on Ramp #1: U1G = J

2.Kinetic energy at bottom of Ramp #1 before traveling across the rough surface: K = J

3.Magnitude of Heat dissipated by friction after traveling across the rough surface: f∆s = J

4.Kinetic energy at bottom of Ramp #2 after traveling across the rough surface: K = J

5.Final gravitational potential energy on Ramp #2 after momentarily stopping: U2G = J

6.The block then slides back down Ramp #2 and across the rough surface to Ramp #1 again. Find the following numerical energy values: Kinetic energy at bottom of Ramp #1 after traveling across the rough surface again: K = J

7.Final gravitational potential energy on Ramp #1 after momentarily stopping: U1G = J

Answer 1

a)

GPE = mgh = 6*9.8* 6= 352.8 J

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b) KE = GPE = 352.8 J

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c)

heat dissipated due to friction

H = uk mg d= 0.5* 6*9.8* 1= 29.4 J

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d)

KE2 = KE - H = 323.4 J

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e)

323.4 = 6*9.8 h

h = 5.5 m

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f)

KE3 = KE2 - 29.4 = 294 J

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g)

GPE = KE3

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