Is the Velocity Calculation Affected by Gravity or Elastic Potential Energy?

[sacred76]

Homework Statement

The spring is compressed with a force of 30 N, calculate the ball’s velocity at point Q when the compressive force is released. The mass of the ball is 300g. (Ignore air resistance).

Relevant Equations

I used mgh = 1/2mv2

Hi all!
I was attempting the following question but my answer differed from the given answer. Please help me to solve it. Thanks.

My answer = 2.45 m/s
Given answer = 3 m/s

 

[berkeman]

Welcome to the PF.

Can you show your work so we can check it?

 

[berkeman]

Also, have you tried using an overall potential energy approach to solve this?

 

[PeroK]

Problem Statement
The spring is compressed with a force of 30 N, calculate the ball’s velocity at point Q when the compressive force is released. The mass of the ball is 300g. (Ignore air resistance).
Relevant Equations
I used mgh = 1/2mv2

Hi all!
I was attempting the following question but my answer differed from the given answer. Please help me to solve it. Thanks.

My answer = 2.45 m/s
Given answer = 3 m/s

What do you think the force of $30N$ involves? Is that the force on the spring? Or is that some force applied to the ball? Are these the same?

Do you want the velocity at point Q or the velocity when the ball is released?

 

[sacred76]

Errr...I'm lost & confused . Please teach me how to do it. TQ

I used mgh = 1/2mv2

Working : mgh = 1/2mv2
m x 10 x 0.3 = 1/2 x m x v2
3 = 1/2v2
v2 = 6
v = 2.45 m/s

 

[haruspex]

Errr...I'm lost & confused . Please teach me how to do it. TQ

I used mgh = 1/2mv2

Working : mgh = 1/2mv2
m x 10 x 0.3 = 1/2 x m x v2
3 = 1/2v2
v2 = 6
v = 2.45 m/s

At point Q, the work done by the spring will be shared between the gained GPE, mgh, and the gained KE. These need not be equal.
What you have found is the KE the ball would have if dropped from point Q to the shown starting position (but with no spring there).

Can you find the energy stored in the spring before release?

 

[sacred76]

At point Q, the work done by the spring will be shared between the gained GPE, mgh, and the gained KE. These need not be equal.
What you have found is the KE the ball would have if dropped from point Q to the shown starting position (but with no spring there).

Can you find the energy stored in the spring before release?

Is it 30 N? Sorry, I'm completely lost here as I can't really comprehend the above. Could you please show me the working/equation for me to digest?

 

[haruspex]

Is it 30 N?

That's a force, not energy.
Calculate the value of the spring constant.

 

[sacred76]

That's a force, not energy.
Calculate the value of the spring constant.

Is it using 1/2Fx?
Elastic potential energy = 1/2 x 30 N x (0.3 m)
= 4.5 J

 

[haruspex]

Is it using 1/2Fx?
Elastic potential energy = 1/2 x 30 N x (0.3 m)
= 4.5 J

Yes, that does it. (If you did not know the Fx/2 formula you could get there by combining F=kx and E=kx²/2.)
So relate that energy to the situation at point Q.

 

[sacred76]

Yes, that does it. (If you did not know the Fx/2 formula you could get there by combining F=kx and E=kx²/2.)
So relate that energy to the situation at point Q.

Can I assume that it's Elastic potential energy = Kinetic energy which is 1/2Fx = 1/2mv²?

 

[PeroK]

Can I assume that it's Elastic potential energy = Kinetic energy which is 1/2Fx = 1/2mv²?

Don't you think that gravity might have something to say about that?