Work Formula
Work is the result when a force acts on an object and moves it by some distance. Sometimes, the direction an object moves is not the same as the direction of the force. In that case, only the component of the force that acts in the direction of the movement causes work to be done. The work formula includes the cosine of the angle between the force and distance for this reason. If the force and movement are in the same direction, than the angle is equal to 0 radians (or 0°). The cosine of zero is: cos0 = 1. The units of work are Joules (J), where 1 J = 1 N∙m = 1 kg∙m2/s2 .
work = force x distance×cosine(the angle between force and movement directions)
W = Fd cosθ
W = work (units J)
k = force (units N)
d = distance (m)
θ = the angle between the force direction and movement direction
Work Formula Questions:
1) A tractor pulled a wagon full of hay a distance of 1000 m. The force exerted on the wagon to move it that distance was 12 000 N. The force acted in the same direction as the movement. Find how much work was done by the tractor to pull the wagon.
Answer: The force and the movement were in the same direction, so the angle between them is 0°. The work can be found using the formula:
W = Fd cosθ
W = Fd cos0
W = Fd(1)
W = (12 000 N)(1000 m)
W = 12 000 000 N∙m
W = 12 000 000 J
The work done by the tractor to move the wagon the given distance was 12 000 000 J, which can also be stated as mega-Joules: 12.0 MJ.
2) A man is pushing a lawn mower across his yard. The force he is applying to the handle of the lawn mower is angled down, 60.0° from the horizontal plane. This force has a magnitude of 900 N. If he pushes the lawn mower 30.0 m, how much work has been done to move the mower?
Answer: The force is at an angle of 60.0° with respect to the movement. The work can be found using the formula:
W = Fd cosθ
W = Fd cos60°
W = Fd(0.5)W = (900 N)(30.0 m)(0.5)
W = 13 500 N∙m
W = 13 500 J
The work done while moving the lawn mower the given distance was 13 500 J.
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