Work, Power and Machine Problems?

Question

I need help on these two problems regarding work, power, and machines:

1. An effort force of 200 N is applied to an ideal machine to move a 750 N resistance a distance of 300 cm.
A) Through what distance must the effort force act?
B) What is the ideal mechanical advantage of the machine?

2. A mover pushes a 260-kg piano on wheels up a ramp 7 m long onto a stage 1.75 m above the floor. The mover pushes the piano with a force of 680 N.
A) How much work does the mover do?
B) What work is done on the piano by the machine?
C) What is the efficiency of the machine?

Thanks for all your help!

Answer 1

1) A.

200Y =750*300

Y =750*300 /200 = 1125 cm.

1) B

M.A = Load / Effort = 750/200 =3.75.

2) A.

Force*distance moved = work done

Work done by the mover = 680 x 7 =4760J.

B)
The piano is lifted through a height of 1.75 m

Work done on the piano is mgh
= 260x9.8x1.75
=4459 J.

C)
Efficiency = 4459/ 4760

Efficiency= 0.93 or 93%.

Answer 2

Not sure about the first one... The second one seems fairly straightforward however. The work the mover does is equilivent to force times distance, or 680 times 7 meters. The machine, in this case, is the ramp, if i am not mistaken. The work the ramp does on the piano is equal to mgh, or (9.8)(260)(1.75). The efficiency should be... one over the sum of the two.

Answer 3

I'll try number 1.
A. In an ideal machine, work in = work out. So
Work in = 200N*d
Work out = 750 N*.3 m
Solve for d.
B. MA = 750 N/200 N

I have to disagree with your first answer for 2C
Efficiency is (useful work) / (energy spent)
So I get
(9.8)(260)(1.75) / 680 times 7 meters