Hooke's Law Problem Set with Word Problems

In summary, the conversation discusses a problem involving a spring-powered projectile launcher and a loaded truck. The first problem involves calculating the energy stored in a compressed spring and the velocity of a projectile launched from the launcher. The second problem involves explaining the phenomenon of a loaded truck sinking lower and bouncing slower than when it is empty, using formulas. The participants also discuss the effect of using a lighter projectile on the momentum and how to show this using algebra.
  • #1
thephysicsm
5
0
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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  • #2
Please answer asap!
 
  • #3
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?
 
  • #4
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..
 
  • #5
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.
 
  • #6
how to show?
 

Related to Hooke's Law Problem Set with Word Problems

1. What is Hooke's Law?

Hooke's Law is a principle in physics that states the force needed to extend or compress a spring by some distance is directly proportional to that distance. This law is named after the English scientist Robert Hooke who first described it in the 17th century.

2. What is the formula for Hooke's Law?

The formula for Hooke's Law is F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its original position.

3. How do I solve problems using Hooke's Law?

To solve a problem using Hooke's Law, you need to know the values of the force applied (F), the spring constant (k), and the displacement (x). You can then plug these values into the formula F = -kx to calculate the force or displacement in the problem.

4. What are some real-world applications of Hooke's Law?

Hooke's Law is commonly used in engineering and design to calculate the amount of force needed to extend or compress springs in machines and structures. It is also used in industries such as automotive and aerospace to design and test materials for their elasticity.

5. Are there any limitations to Hooke's Law?

While Hooke's Law is a useful principle, it does have some limitations. It only applies to linear springs, meaning the force and displacement must be directly proportional. It also assumes that the spring is being extended or compressed within its elastic limit, meaning it will return to its original shape after the force is removed.

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