# Using an electric winch to compress a spring and launch an object

I'm having trouble grokking the relationship between a winch's pull/torque and a spring's potential energy.

I would like to compress a spring using an electric winch and figure out how far it will be able to launch an object.

1. If the spring's maximum load is higher than the winch's force, do the other details of the spring even matter? Specifically, if the electric winch has 2000-lbs of pull, is the maximum potential energy it can store in the spring 2000-lbs (8896-N) of force, regardless of the spring's length or constant?

2. What is the correct formula for finding the height which the spring will launch an object (of let's say 1-pound) straight into the air (after it has been compressed up to the winch's max pull of 2000-lbs)?

The energy stored in the spring is equal to the work done in compressing it. The force needed to compress the spring to the maximum is only a small part of this calculation.

Suppose the spring is completely relaxed, and you apply a small force compressing the spring slightly. The energy stored is the product of the force and the distance, measured in Newton-metres, or joules.

Now you increase the force slightly, and the spring compresses a short distance more. The additional energy stored in this new force multiplied by this next compression distance.

This continues, until the spring is totally compressed. So to calculate the energy stored, you need to know how far the spring compresses, and how the compression force changes as the spring compresses.

Edit to rely to comment:

Suppose the spring is quite long in its relaxed state, with a spring constant of 40 lbf/in. The spring will need to compress by 50 in, to reach the winch maximum of 2000 lbf.. So the energy stored in the compressed spring would be (with suitable conversion to SI) $$E_s=\frac12kx^2=\frac127005\times1.27^2=5650 \text{ joules}$$

So this would be the energy available to loft a projectile. The problem would be to transfer as much as possible of this energy to a light projectile. There are inherent, internal losses in the rapid extension of a spring that make it difficult to efficiently launch a missile. Usually, the spring pushes slowly, with huge force on the short end of a lever, while a light mass accelerates quickly at the long end of the lever.

Google "trebuchet", or even "punkin chuckin". Spelling is correct!

The equation in the comment would give the maximum height possible, with no losses in the spring.

• Thank you! So let's say I know the spring constant is 40 lbs/in (4.5 N/m). The winch has 2000-lbs of pull. Is there a way to use Hooke's to solve for the distance the spring will compress? From there, will the following equation correctly tell me how far the spring will launch a 1-pound (0.45 kg) object? 0 + ½ (4.5 N/m) Xm² = 0 + (0.45 kg) (9.8 m/s²) h Commented Mar 18, 2014 at 21:14
• Thank you so so much. This clears up a ton! So one last sanity check if you don't mind: With the above assumptions, the maximum launch height comes in at 1,281 meters, correct? From there, is there a formula or rule-of-thumb to find the actual height with losses in the spring? Commented Mar 19, 2014 at 1:41
1. I am assuming that by 'winch's force' you mean the maximum force that can be generated by the torque produced in the winch. If this force is not higher than the load, then no it cannot pull it. The maximum potential energy the winch can hold depends on how much turns it is given, the properties of the spring are totally irrelevant here.

2. w = mgh where m is the mass of the object, h is the maximum height and w is the work done to completely compress the spring.

• if the winch is generating more force than the spring exerts to resist compression, where does the extra force go? Commented Mar 18, 2014 at 19:43
• If it's more, it will compress the spring. Not sure what you mean by extra force. You mean if it's more than the force required to completely compress it? Then the same place where your force goes when you try to push a solid building.
– user42733
Commented Mar 18, 2014 at 19:51
• Newton's Third says that at any time, the force exerted by the winch on the spring is equal to the force exerted by the spring on the winch. Spring force is the force needed to compress it and is constantly changing as the spring compresses, so that's all the winch can exert... Commented Mar 18, 2014 at 21:11