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A plank of wood is used to help lift a heavy box of weight 500 N into the back of a truck as shown in figurebelow. The plank is 10 m long and the object rises a vertical height of 2m. A force of 200 N is used to pull the object along the plank.(a) Determine the change in gravitational potential energy ofthe box as it is lifted into the truck.ans= 1000J(b) How much work is done by the 200 N force?ans=400J(c) Calculate the efficiency of the set up.??

A plank of wood is used to help lift a heavy box of weight 500 N into the back of a truck as shown in figurebelow The plank is 10 m long and the object rises a class=

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ANSWERS

(a) 1000 J

(b) 2000 J

(c) 50%

EXPLANATION

Given:

• The weight of the box, Fg = 500 N

,

• The length of the plank, l = 10 m

,

• The vertical height of the truck, h = 2 m

,

• The force applied to pull the box, F = 200 N

Find:

• (a), The change in gravitational potential energy, PE

,

• (b), The work done by the 200 N force, W

,

• (c), The efficiency of the set up

(a) The change in gravitational potential energy is,

[tex]PE=mgh[/tex]

The product mg is the weight of the box,

[tex]PE=500N\cdot2m=1000J[/tex]

Hence, the change in gravitational potential energy of the box is 1000 J.

(b) The 200 N force is applied along the plank, so the distance it is applied for is the length of the plank and, therefore, the work done by this force is,

[tex]W=200N\cdot10m=2000J[/tex]

Hence, the work done by the 200 N force is 2000 J.

(c) The efficiency is the quotient between the output work - which is the work needed to do the job, and the input work - which is the work done,

[tex]efficiency=\frac{W_{output}}{W_{input}}\cdot100=\frac{1000J}{2000J}\cdot100=0.5\cdot100=50\%[/tex]

Hence, the efficiency is 50%.

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