A 230 kg piano rests on the ground; you want to get it into the back of a moving

Question

A 230 kg piano rests on the ground; you want to get it into the back of a moving truck 1.0meter above the ground. You do NOT need to show your work for this problem. How much force would you (and your friends) need to exert on the piano if you lift it straight up through 1.0m at constant speed? How much force would you need to exert on the piano to push it up a frictionless 10.' ramp to a final vertical height of 10m at constant speed? What is the mechanical advantage of using the ramp in part (b), compared to lifting the piano straight up? How much work would you (and your friends) do on the piano by lifting it straight up in part (a)? How much work would you do on the piano by pushing it completely up the ramp in part (b)?

Explanation / Answer

here,

mass of piano, m = 230 kg
height, h = 1 m
Using g = 10 m/s^2

Part A:
From Newton Second Law, Fnet = 0
F = mg
F = 230 * 10
F = 2300 N

Part B:
angle of ramp, A = 10 degrees

From Newton Second Law, Fnet = 0
F - mgSinA = 0
F = 230 * 10 * Sin10
F = 390 N

Part C:
Using a ramp will decrease Net applied force requirement, so there will be less work done

F1/F2 = 2300/390 = 5.8

Part D:
From Work Energy Theroam, Work done in lifting = gain in potential Energy
w = mg*h
w = 230 * 10* 1
w = 2300 J

Part E:
Work Done = Force * Displacement*Cos0
W = F*h/sinA
W = 390*(1/Sin10)
W = 2300 J

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