Thomas the tank Engine Calvin has constructed a track for his toy train, as show

Question

Thomas the tank Engine Calvin has constructed a track for his toy train, as shown in the figure below. The train has mass of 0.2 kg. The upper part of the track is h = 0.1 m above the floor. Assume the track is frictionless. The train is initially at rest on the upper part of the track. Calvin pushes it 0.3 m horizontally. In order to get the train moving with a velocity of 1.5 m/s, how much force much must he apply? The train, now with velocity 1.5 m/s, then rolls down the slope to the lower section of track. Once it reaches the floor, what is the train's new velocity?

Explanation / Answer

intial PE = mgh = 0.2 * 9.8 * 0.1 + 0.5 mv^2

PE = E = 0.196 + 0.5 * 0.2* 1.5^2

now from Work eenrgy theoren

W = Fs = 0.421

Force F = 0.421/0.3

F = 1.403 N
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change in KE = PE

0.5 m *(Vf^2 - Vi^2) = 0.196

0.5* 0.2 * (1.5^2 - V^2) = 0.196

v = 1.5 + 0.538 = 2.038 m/s

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