How much work is done by gravity in the process?

Question

A person lifts a 3.8 kg cement block a vertical distance of 1.42 m and then carries the block horizontally a distance of 10.30 m.

Answer 1

Zero work was done by gravity. The work was done against gravity.

If a person lifted the block and carried it and a distance and then placed it on the level then no work was done by gravity.
When the block fall, then it is a different story.
The person did work against gravity however is

W= mgh= 3.8 x 9.81 x 1.42=53 J

Work is not a vector quantity.

Answer 2

Work is defined as force times displacement times the cosine of the angle of the displacement relative to the direction of the force. The force in this case is gravity and the direction of the displacement is 180 degrees relative to the direction of the force of gravity. Thus, the equation during the lift is:

3.8*9.8*1.42*cos(180)
= -52.9 J
The answer is negative not because work is a vector (it isn't) but because the work done by gravity is negative.

For the horizontal displacement, the equation becomes:

3.8*9.8*1.42*cos(90)

The angle between the force and the displacement is 90 degrees. Cosine of 90 degrees is zero so no work is done by gravity during the horizontal displacement.

Answer 3

Work done by gravity, is F(weight) x s(displacement)

displacement should be in the vertical direction, because the weight force acts in this direction.

F(weight) = 3.8 x 9.81 = 37.28 N
This force acts over the distance which it is lifted up, but in opposite direction so we will have negative work....(weight force acts opposite to action)
Work done = F(weight) x s
= 37.28 x (-1.42)
= - 52.94 J

So work is done against gravity, thats true, and I was incorrect about calling work a vector, because i remember that the scalar multiple of two vectors is a scalar (apologies), but if work is done against gravity, im assuming it to be acceptable to say that negative work has been done by gravity, although it doesnt make much sense i know...

Although a weight force still acts over the horizontal transfer, gravity does no work on it as its vertical height remains the same.

Answer 4

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RE:
How much work is done by gravity in the process?
A person lifts a 3.8 kg cement block a vertical distance of 1.42 m and then carries the block horizontally a distance of 10.30 m.

Answer 5

This is a work function problem. Work energy = WE = Fd; where F is force and d is a distance covered in the direction of the force. [I call it work energy to remind us that work is energy just like kinetic and potential energy are energies.]

In your case, F = mg, which is gravitational force on a mass m and g is the acceleration due to gravity (9.81 m/sec^2 on Earth's surface). We call gravitational force weight W = F = mg.

Thus WE = Fd = Wd = mgd up to this point. What's d? Its the distance the block is moved against the force of gravity. As gravity acts in the up down direction only, d = h = height, which is the vertical distance = 1.42 meters. Then WE = mgh; where m = 3.8 kg, g = 9.81 m/sec^2, and h = 1.42 m for the work done in lifting the block. You can do the math.

Now for the WE in carrying the block d = 10.30. Again we have WE = Fd; and d is given. What's the force? Well we don't know that do we. In fact, nothing is given to find the force F. So, this question assumes no force F; so that WE = Fd = 0*10.30 = 0 and, ta da, there is no work done in carrying the block horizontally. That follows because we assumed no force acting in the horizontal direction.

Of course, this is an unrealistic problem. There is clearly horizontal force F. In fact, it's the force of static friction as your person's feet push off in the horizontal direction to propel himself and the block he carries. There would in fact be work done against that frictional force in a real world.

But this is an unrealistic problem. It's purpose is to point out that there has to be both force and distance for WE to exist. In this case weight was the force against which work was done; and weight is a vertical force, so the distance moved is height. And WE = 0 in the horizontal direction because we assumed F = 0. [Which is unrealistic; imagine how far we'd walk on a frictionless surface.]

Answer 6

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Answer 7

Work is done by gravity only during lifting. No work is done in carrying horizontally.
Work done
= mgh
= (3.8) * (9.8) * (1.42) J
= 52.9 J

Answer 8

The work done by gravity is : W = - m g h .
W = - 3.8*9.8*1.42 = 52.88 J.