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).