# Collision of block with spring w/ friction

• Selophane
In summary, a 4.20 kg block collides with a horizontal spring with a spring constant of 270 N/m, causing the spring to compress a maximum distance of 4.00 cm. The coefficient of kinetic friction between the block and the surface is 0.250. The work done by the spring in bringing the block to rest is 0.216 J, but the answer is marked as incorrect. The work done by friction is 0.412 J, and the speed of the block when it hits the spring can be found using the total energy equation. The answer to part a may need to be negative, as indicated by the answer to part c being marked as incorrect when using the positive value.
Selophane
A moving 4.20 kg block collides with a horizontal spring whose spring constant is 270 N/m. The block compresses the spring a maximum distance of 4.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.250. What is the work done by the spring in bringing the block to rest?

When I first tried this I assumed it was simply:

W = 0.5kx^2 = (0.5)(270)(0.04)^2 = 0.216 J

However the answer is not matching with the correct one, not sure where i went wrong on such a simple problem... sorry if this is too easy, which I'm sure it is...

btw, there is a 2nd and 3rd part of the question

2nd part:

How much mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring?

I got this one right, simply: W = Ffs = (4.2)(9.81)(0.25)(0.04) = 0.412 J

finally, part 3:

What is the speed of the block when it hits the spring?

now i tried simply using (work of friction) = 0.5mv^2 but am not getting correct answer?

Thanks,
Chris

Selophane said:
A moving 4.20 kg block collides with a horizontal spring whose spring constant is 270 N/m. The block compresses the spring a maximum distance of 4.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.250. What is the work done by the spring in bringing the block to rest?

When I first tried this I assumed it was simply:

W = 0.5kx^2 = (0.5)(270)(0.04)^2 = 0.216 J

However the answer is not matching with the correct one, not sure where i went wrong on such a simple problem... sorry if this is too easy, which I'm sure it is...

btw, there is a 2nd and 3rd part of the question

2nd part:

How much mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring?

I got this one right, simply: W = Ffs = (4.2)(9.81)(0.25)(0.04) = 0.412 J

finally, part 3:

What is the speed of the block when it hits the spring?

now i tried simply using (work of friction) = 0.5mv^2 but am not getting correct answer?

Thanks,
Chris
I get the same answer you do for part a.
For part c, what happened to the work done by the spring (its Potential Energy change) in your equation?

Thanks for the prompt response!

Well glad to see I'm not crazy and kept getting same answer for A, but it's saying it is not correct (this is an online assignment)

For C, i assumed the spring didn't matter since it was just as it hit the spring? Perhaps I'm misunderstanding the problem. And if i do need to use answer from A, i cannot get correct answer since it is still giving our answer as incorrect.

thanks again,
Chris

Selophane said:
Thanks for the prompt response!

Well glad to see I'm not crazy and kept getting same answer for A, but it's saying it is not correct (this is an online assignment)

For C, i assumed the spring didn't matter since it was just as it hit the spring? Perhaps I'm misunderstanding the problem. And if i do need to use answer from A, i cannot get correct answer since it is still giving our answer as incorrect.

thanks again,
Chris
The total energy equation is
Inititial mech. energy - work done by friction = final mech. energy

Since initially there is no PE, and in the end, no KE, then
KE_i -W_f = PE_f
1/2mv^2 - W_f = 1/2kx^2

You've already solved W_f and 1/2kx^2, so now solve for v.

BTW, the work done by a conservative force (like a spring force or gravity force) is equal to the change in PE. So your answer to part a is correct. What makes you think it is not, the book answer? Maybe you're a bit smarter than the book, yes?

ah, thanks for the clarification on C, however this is an online assignment and it does say 0.216 J is wrong for A, and well I can't do much if its saying its incorrect, I'll have to let the teacher know I guess, thanks again, much appreciated!

-Chris

If the spring compresses, why won't it uncompress, push the block away? Friction will do the job of stopping it.

Selophane said:
ah, thanks for the clarification on C, however this is an online assignment and it does say 0.216 J is wrong for A, and well I can't do much if its saying its incorrect, I'll have to let the teacher know I guess, thanks again, much appreciated!

-Chris
Ahh, try -.216J. That minus sign will do it. Sneaky!

## 1. What is the definition of "Collision of block with spring w/ friction"?

"Collision of block with spring w/ friction" refers to a scenario in which a block collides with a spring, causing the spring to compress or stretch. This collision includes the presence of friction, which affects the motion of the block and the spring.

## 2. How does friction affect the collision of the block with the spring?

Friction plays a significant role in the collision of the block with the spring. It causes the block to experience a resistive force, which decreases its velocity and energy during the collision. Friction also affects the compression or stretch of the spring, resulting in a different outcome compared to a frictionless collision.

## 3. What are the factors that affect the outcome of the collision between the block and the spring?

Several factors affect the outcome of the collision, including the mass and velocity of the block, the stiffness of the spring, and the coefficient of friction between the block and the surface it is on. These factors determine how much energy is transferred between the block and the spring during the collision.

## 4. How can the collision of block with spring w/ friction be modeled mathematically?

The collision of block with spring w/ friction can be modeled using the laws of conservation of energy and momentum. This involves calculating the initial and final energies and momentums of the block and the spring, taking into account the work done by friction. The resulting equations can then be solved to determine the final positions and velocities of the block and the spring.

## 5. What real-life applications involve the collision of block with spring w/ friction?

One real-life application of this scenario is in car suspensions, where the movement of the car's wheels over uneven surfaces causes the springs in the suspension to compress and stretch. Friction plays a role in this process, affecting the ride comfort and handling of the car. Another application is in sports, such as in the bouncing of a basketball on the ground, which involves the collision between the ball and the surface, as well as the friction between them.

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