Cart weighs 1kg, h = 5m, d (bottom length) = 10m. a) Use the path ac to raise th

Question

Cart weighs 1kg, h = 5m, d (bottom length) = 10m.

a) Use the path ac to raise the cart up an inclined plane that makes an angle of about 30 degrees with the earth's surface. Calculate the work you performed using the definition of work.

b) Raise the cart directly to the same height as the top of the inclined plane along path ad and then move the cart horizontally from point d to point c. Again, use the definition of work to calculate the work done in raising the cart along path adc.

c) How does the work measured in a compare to that measured in b? Hint: Is the force conservative?

Show all work. Thank you!

Explanation / Answer

work done = force applied*displacement*cosalpha

part(a)

force applied = F = m*g*sintheta   up the incline plane

displacement = d = 10 m

alpha = 0

workdone Wac = m*g*sintheta*d = 1*9.8*sin30*10 = 49 J

part(b)

work done = Wad + Wdc

Wad = F*h*cos0

force = m*g

Wad = m*g*h* = 1*9.8*5 = 49 J

Wdc = F*dc*cosalpha

as the cart is moved from d to c the anlge between force and displacement alpha = 90

Wdc = 0

Wadc = Wad + Wdc = 49 J

=====================

part(a)

work done in a = work done in b

the work remains in any path from a to c

force is conservative

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