The mass of the cart is 500g. the length of the ramp is 1.20m What is the height

Question

The mass of the cart is 500g. the length of the ramp is 1.20m What is the height of the incline? What is the GPE energy at the very top? What is the maximum speed at the very bottom? A ball of mass 5.0 kg is lifted off the floor a distance of 1.7 m. What is the gravitational potential energy of the ball at this height? Now the ball is released from rest and falls to the floor. What is the kinetic energy of the ball just before it hits the floor? Explain with & without calculation. What is its maximum velocity before hitting the floor? A car of mass 1000 kg is at the top of a 10 degrees hill as shown. What is its gravitational potential energy of the car relative to the bottom of the hill? What will its kinetic energy be when it reaches the bottom?

Explanation / Answer

a)Using trigonometry

H/1.2 = sin15

H = 1.2 x sin15 = 0.311 m

Hence, H = 0.311 m

b)PE is given by

PE = m g h

PE = 500 x 10^-3 x 9.8 x 0.311 = 1.524 J

Hence, GPE = 1.524 J

c)from conservation of enegy

KE(bottom) = PE(top)

1/2 m v^2 = m g h

v = sqrt (2 g h)

v = sqrt (2 x 9.8 x 0.311) = 2.468 m/s

Hence, v = 2.468 m/s

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