A spring is used to propel a 200-g steel ball along a track that includes a ramp

Question

A spring is used to propel a 200-g steel ball along a track that includes a ramp as shown. The ball is pushed to the left, compressing the spring (“point A”), and is then released and allowed to roll along the track. The horizontal portions of the track are smooth (frictionless), while the slanted ramp is rough.(a) After it is released, the ball’s speed on the horizontal section of the track is 4.20 m/s. When the ball reaches the top of the ramp (“point C” at a height of 30 cm), its speed is 1.60 m/s. Use conservation of energy between points B and C to determine the work done on the ball by friction. (b) What is the average magnitude of the force of friction on the ball? (Hint: first find the length of the slanted portion of the track; this is the distance over which friction acts.)

Explanation / Answer

a) Conservation of energy:

1/2 mVB2=1/2 mVc2 + mgh + Wf

Wf=(0.2*4.22)/2 - (0.2*1.62)/2 - (0.2*9.81*0.3)

Wf= 0.9194 J

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b)

To find the length of the slanted portion of the track we need the angle of the ramp:

sin(theta) = 0.3/x

x= 0.3/sin(theta)

with this value:

Wf= Ff * x

Force of friction:

Ff = Wf / x

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