Hooke's Law Problem Set with Word Problems

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Homework Help Overview

The discussion revolves around a problem set related to Hooke's Law, specifically focusing on a spring-powered projectile launcher and the effects of mass on momentum and spring compression. Participants are exploring the energy stored in a compressed spring and the behavior of a truck under load.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to calculate the energy stored in the spring and the speed of a projectile. Questions are raised regarding the relationship between mass and momentum, with a request for algebraic proof. The effects of loading a truck on its bounce and compression are also being discussed.

Discussion Status

Some participants have provided calculations and expressed their thoughts on momentum conservation. There is ongoing exploration of the implications of mass on momentum and the behavior of the truck under load, with hints provided to guide further reasoning.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the depth of discussion regarding solutions. The original poster has posed specific questions that require clarification and exploration of underlying principles.

thephysicsm
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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.
 
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Please answer asap!
 
thephysicsm said:
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?
 
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..
 
thephysicsm said:
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.
 
how to show?
 

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