Question 1 A spring is compressed 0.250 m and launches a 3.00 kg object across f
ID: 1786558 • Letter: Q
Question
Question 1
A spring is compressed 0.250 m and launches a 3.00 kg object across frictionless ice. After some distance, the object hits a rough patch of ice where the coefficient of kinetic friction of the object on the surface is 0.0500. If the spring constant of the spring is 157 N/m, find the distance the object travels across the rough patch of ice using work and energy.
Question 2
A 1790 kg car is traveling 42.5 m/s when it comes up to the bottom of a 8.00° hill. If the car coasts up the hill and the coefficient of rolling friction is 0.450, how far up the hill will the car travel?
Explanation / Answer
Spring potential energy = 0.5kx^2.
Work done by friction = µ*mgd.
Spring potential energy = Work done by friction
0.5kx^2 = µ*mgd.
Therefore d = kx^2 / 2(µ)mg
= 157*0.25^2 / 2*0.05*3*9.8
= 3.34 m.
Q-2)
Force acting down the hill due to gravity = mg(sin 8)
= 2441.4 N
Normal force of slope on car = mg(cos 5)
= 17,371.3 N.
Friction encountered = (17,371.3 x 0.45) = 7817 N.
Total accelerating force = (7817 + 2441.4) = 10258.5 N
Acceleration = (f/m) = (10258.5/1,790) = 5.73 m/sec^2.
Distance to stop = (v^2/2a)
= (42.5^2 / 2*5.73)
= 157.6 metres.
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