A constant net force of 410 N is applied upward to a stone that weighs 32 N. The upward force is applied ...?

Question

A constant net force of 410 N is applied upward to a stone that weighs 32 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?

Please help me with this problem.
I'm having trouble solving it.

Answer 1

use vf^2 = v0^2 + 2as
where vf is the final velocity
v0 is the initial velocity (zero)
a is acceleration = f/m = 410/32
s is the distance, 2 m

so vf^2, the speed of the stone as you release it, is
2*2*410/32 or 410/8
so vf = sqrt(410/8)

Now, if you toss a stone upward at an initial speed of 410/8 m/s, how much higher will it rise?
Well, first you need to compute how LONG it will rise, in time.
Since acceleration is -9.8, the speed will be zero when 9.8t = sqrt(410/8), or t = sqrt(410/8)/9.8 seconds.

Finally, use the formula s = v0t+.5 at^2 to compute the distance:

s = sqrt(410/8) * t - .5*9.8 t^2
where t = sqrt(410/8)/9.8

Answer 2

Work done by the force(410N) on the stone=410*2=820 Joules Increase in the energy of the stone= Increase in P.E + Kinetic energy K gained. = 32*2 +K = 64+K Joules. Equating the two: 64+K = 820 which gives K = 756 Joules. Suppose the stone rises up a distance h meters from the position of release to the highest point where it comes to rest. Then the Kinetic energy of the stone changes into its Potential Energy. So: 32h =756 which gives h=756/32 =23.625 m Answer

Answer 3

Figure out the net acceleration, requires taking the difference between the applied force and the weight

Figure out the net acceleration. Given the distance, you can figure out how long it took. This allows you to then calculate the velocity, which you can use to figure out the kinetic energy.

The kinetic energy is converted to potential energy, allowing you to figure out the maximum height.

Answer 4

∆E = W = Fs = (410 - 32)(2) = 756 J
∆E = mgh
h = 756/32
h = 23.625 m