# A constant net force of 385 N is applied upward to a stone that weighs 28 N. The upward force is applied through a distance of 2.0 m, and the stone is then released. To what height, from the point of release, will the stone rise?

what formulas?

## The answer depends upon whether the "net applied force", which I will call F', includes the weight, W. I will assume that it does not. F' -W is the true net force, including weight.

Work done accelerating the stone is

F*x = (F' - W)*x = (385-28)* 2.0 = 714 Joules. That will equal the kinetic energy at release. Set it equal to

Work = M g h = Weight* h to compute the additional distance that it rises, h.

## To solve this problem, you can use the work-energy principle and the concept of potential energy. The formulas you will need are:

1. Work (W) = Force (F) x Distance (d)

2. Gravitational potential energy (PE) = mass (m) x acceleration due to gravity (g) x height (h)

3. Net work done (W_net) = change in potential energy (ΔPE)

Here's how you can apply these formulas to solve the problem:

1. Calculate the work done by the upward force on the stone. Since the force is constant and in the same direction as the displacement, the work done is given by:

W = F x d

W = 385 N x 2.0 m

2. Calculate the change in potential energy of the stone. When the stone rises, its potential energy increases. The change in potential energy is given by:

ΔPE = m x g x h

In this case, the mass of the stone is 28 N (weight) divided by the acceleration due to gravity (approximately 9.8 m/s^2), so m = 28 N / 9.8 m/s^2.

3. By the work-energy principle, the work done (W) is equal to the change in potential energy (ΔPE). Therefore:

W_net = ΔPE

385 N x 2.0 m = m x g x h

4. Rearrange the equation to solve for the height (h):

h = (385 N x 2.0 m) / (m x g)

Now, substitute the value for mass (28 N / 9.8 m/s^2) into the equation to find the height (h).