Show your work and include units with your answers for full credit. A spring is

Question

Show your work and include units with your answers for full credit. A spring is used lo propel a 200-g steel hall along a track that includes a ramp as shown. The hall 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). w while the slanted ramp is rough. 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 in 1.60 m/s. Use conservation of energy between points B and C to determine the work done on the hall by friction. What is the average magnitude of the force of friction on the boll?

Explanation / Answer

from the work energy theorem

W = change in kinetic energy

W = 1/2 * mv1^2 - 1/2 * m v2^2

= 1/2 * 0.2 kg (( 4.2 )^2-(1.6 )^2

=1.508 J

work done is

W = fs

s can be found by using pythogarous theorem

s = root ( (0.4)^2 + ( 0.3 )^2 = 0.5 m

f = W/s = 1.508 J/0.5 m = 3.016 N

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