A 3.00-kg particle moves from the origin to position C , having coordinates x =

Question

A 3.00-kg particle moves from the origin to position C, having coordinates x = 6.50 m and y = 6.50 m (see figure below). One force on the particle is the gravitational force acting in the negative y direction.

(a) the purple path (OAC)
  J

(b) the red path (OBC)
J

(c) the blue path (OC)
J

Please help,,.

A 3.00-kg particle moves from the origin to position C, having coordinates x = 6.50 m and y = 6.50 m (see figure below). One force on the particle is the gravitational force acting in the negative y direction. r , calculate the work done by the gravitational force on the particle as it goes from O to C along the following paths. (a) the purple path (OAC) J (b) the red path (OBC) J (c) the blue path (OC) J Please help,,. F Using the equation W = F?r cos ? =

Explanation / Answer

Realize that the work done by gravity is alligned vertically along the y-axis. In other words, we don't care what the horizontal, x, component is as any work done in the x direction will not be done by gravity.

Then realize that work is equal to force * distance, W=f*d.

What is the force of gravity acting on the particle?

The particle's mass is 3.00kg. g= accelleration = -9.8m/s^2.

force = mass * acelleration

f = 3.00kg * -9.8m/s^2

f = -29.4 N

We have the force. Now we need the distance traveled in the y direction.

It starts at the origin, y=0. It ends at 6.5m.

W = f * d

W = -29.4N * 6.5m

W = 191.1 J

Regardless of which path you take, the change in the y-component/height will be the same so the work done is independent of the path. i.e. a, b, and c are all 191.1 J

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