Hooke's Law Problem Set with Word Problems

[thephysicsm]

Hello all,

I am currently working at a problem that is (seems) simple at calculations but I am puzzled by the word problems.

The problems are:

1. A spring powered projectile launcher contains a spring with:

k=300 N/m

The spring is compressed by 15.0 cm.

a. How much energy is stored in the compressed spring?

My answer is: 1/2 kx^2, and the answer is about 3.375J

b. How fast would a 38 g projectile be traveling if it were shot by this projectile launcher?

my answer is 13.3278 m/s

So my question is: would using a lighter projectile provide more momentum or less? Prove the statement algebraically.

Second question is: a truck sinks lower when you load it and it bounces slowly when it is loaded than when it is empty. Explain these phenomena using formulas.

 

[thephysicsm]

Please answer asap!

 

[Doc Al]

a. How much energy is stored in the compressed spring?

My answer is: 1/2 kx^2, and the answer is about 3.375J

b. How fast would a 38 g projectile be traveling if it were shot by this projectile launcher?

my answer is 13.3278 m/s

Looks good.

So my question is: would using a lighter projectile provide more momentum or less? Prove the statement algebraically.

What do you think? Hint: What remains constant, regardless of the mass of the projectile?

Second question is: a truck sinks lower when you load it and it bounces slowly when it is loaded than when it is empty. Explain these phenomena using formulas.

What do you think?

 

[thephysicsm]

I think the momentum would remain constant right?

I don't really know about the second question but I have a somewhat guess:

The more mass there is on the truck, the truck bounces less than it is not loaded. Or there will be no difference since the springs in a truck will compress..

 

[Doc Al]

I think the momentum would remain constant right?

Whether the momentum changes is what you need to show. What remains constant for any projectile launched from this compressed spring?

I don't really know about the second question but I have a somewhat guess:

The more mass there is on the truck, the truck bounces less than it is not loaded. Or there will be no difference since the springs in a truck will compress..

Pick one!

The fact that a loaded truck sinks more should make sense from Hooke's law.

 

[thephysicsm]

how to show?