Calculating Initial Energy of a Spring-Connected Mass

[Raghav Gupta]

Homework Statement

A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest.
After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 m/s. The total initial energy of the spring is:
1.5 J
0.6 J
0.3 J
0.8 J

Homework Equations

Spring potential energy is 1/2 kx²
In this question we have to do basically energy balance

The Attempt at a Solution

Isn't this question wrong?
We should be given other block mass and told that it is an elastic collision?

 

[AlephNumbers]

Why don't you post your work so we can see what you have so far. It is solvable.

 

[Raghav Gupta]

Why don't you post your work so we can see what you have so far. Even if it were wrong, it would be a good exercise.

Initial energy = 1/2 kx²
At x/2 distance,
1/2 kx² = 1/2 kx²/4 + 1/2 mv²
Now we know the mass of the block which is colliding but don't know velocity at that instant of colliding.
If we have been told that other block has same mass and it is an elastic collision then v could be 3m/s ?

 

[AlephNumbers]

Now we know the mass of the block which is colliding but don't know velocity at that instant of colliding.
If we have been told that other block has same mass and it is an elastic collision then v could be 3m/s ?

If the first block stops moving after colliding with the second block, and the second block continues forward with a velocity, then I think it is safe to assume an elastic collision. Although it would have been nice if they had specified that it was an elastic collision in the problem statement.

Your work looks good so far. What do you know about elastic collisions?

 

[Raghav Gupta]

If the first block stops moving after colliding with the second block, and the second block continues forward with a velocity, then I think it is safe to assume an elastic collision. Although it would have been nice if they had specified that it was an elastic collision in the problem statement.

Your work looks good so far. What do you know about elastic collisions?

In elastic collisions momentum and energy are balanced initially and finally.
If two blocks should have same velocity one transferring other, then masses should be same.
But they have not given that.

 

[AlephNumbers]

In elastic collisions momentum and energy are balanced initially and finally.

Bingo!

If two blocks should have same velocity one transferring other, then masses should be same.
But they have not given that.

Set up the conservation of momentum equation and the conservation of energy equation. You have two unknowns, and two equations relating those two unknowns.

 

[Raghav Gupta]

Momentum conservation applying
0.1 v = 3m
Applying energy balance
1/2 * 0.1v² = 9/2 m
Yeah v = 3m/s
But as I say, how we are assuming elastic collision?

 

[AlephNumbers]

Well, they really should have specified. They obviously want you to treat the collision as perfectly elastic, because they don't mention any energy being lost due to non-conservative forces (such as friction). But really, I guess we don't know. It is the fault of whoever made this question.

 

[Raghav Gupta]

Thanks.