A 6 kg cart starting from rest rolls down a hill and at the bottom has a speed of 10 m/s. What is the height of the hill?
1 answer:
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Answer:
26b) 66.7%
27) 500 N
Explanation:
26.a) In a two pulley system, the load is attached to one of the pulleys. The other pulley is attached to a fixed surface, as well as one end of the rope. The other end of the rope goes around moving pulley, then around the fixed pulley.
26.b) Mechanical advantage is the ratio between the forces:
MA = load force / effort force
Efficiency is the ratio between the work:
e = work done on load / work done by effort
Work is force times distance.
e = (F load × d load) / (F effort × d effort)
Rearranging:
e = (F load / F effort) × (d load / d effort)
e = MA × (d load / d effort)
In a two pulley system, the load moves half the distance of the effort. So the efficiency is:
e = (4/3) × (1/2)
e = 2/3
e = 66.7%
27) In a three pulley system, the load moves a third of the distance of the effort.
e = (F load / F effort) × (d load / d effort)
0.40 = (600 N / F) × (1/3)
F = 500 N
