# Homework Help: Conservation of Energy -- Toy car hits and compresses a spring

1. Jan 1, 2018

### Fatima Hasan

1. The problem statement, all variables and given/known data
A toy car has a mass of 2 kg moves with initial speed of 2 m/s on a rough horizontal plane of μκ=0.14.A spring with constant of 250 N/m is fixed. Which of the following statements is true ?
A) The toy does not approach the spring
B) The toy just touch the spring[/url][/IMG]
C) The toy compress the spring
D) The toy back with constant speed on the surface

2. Relevant equations
ΣF = ma
Fκ = μκ FN

3. The attempt at a solution
ΣF = ma
-Fκ = ma
Fκ = μκ FN
a = - μκg = -0.14 * 10 = - 1.4 m/s^2
vƒ^2 = vi^2 + 2 a d
= 4 - 2*1.4*3 = - 4.4 (negative) --> A) The toy does not approach the spring.
Can somebody check my answer please ?

2. Jan 1, 2018

### PeroK

I think you have missed out some information from the question. The car is moving towards the spring, but you don't say how far away it is.

3. Jan 1, 2018

### Fatima Hasan

d = 3 m

Last edited: Jan 1, 2018
4. Jan 1, 2018

### PeroK

That's a strange way to do things. Surely you ought to solve for $d$ and see whether it is less than $3m$?

5. Jan 1, 2018

### Fatima Hasan

which law to use??

6. Jan 1, 2018

### PeroK

You've got the correct equations. What you did was calculate the velocity squared when the car had moved $3m$. You got a negative answer and concluded that the car doesn't move $3m$. This is not wrong, but it seems illogical to me. I would have calculated how far the car moved before it stopped. That just seems a lot more logical.

7. Jan 2, 2018

### haruspex

Strange question... Are the wheels of the toy car stuck? Is there anything else you have left out?

8. Jan 2, 2018

No

9. Jan 2, 2018

### haruspex

Then why does the friction of the surface matter?

10. Jan 2, 2018

### Fatima Hasan

I haven't missed out anything else . There is a friction between the wheels and the surface . I got the answer by finding the distance , and it was less than 3 m , so the correct answer is A .

11. Jan 2, 2018

### Delta²

The wheels have to be perfect circles in order for friction not to do any work..

12. Jan 2, 2018

### haruspex

If the wheels are turning, the friction between them and the surface is irrelevant. It is rolling contact.
There will be friction in the wheel axles, and some rolling resistance (look that up).
If the wheels do not skid then no work is done against friction.

13. Jan 2, 2018

### PeroK

Given that some toy cars don't have wheels that actually rotate, it's impossible to agree on what the question actually intended. It's difficult to imagine a toy car on a rough surface without significant resisting forces. I suspect, therefore, that the OP solved the question as intended.

14. Jan 2, 2018

### haruspex

Perhaps, but I feel it is important that Fatima is not left with the misunderstanding that this is just standard friction. It is a common blunder.
Your argument would be more reasonable if the question did not specifically refer to "μk".
There is also the possibility that it is a trick question. This is made more likely by the list of alternatives beyond "the car does not reach the spring". Why have a spring? Why not just ask whether the car reaches some point?
@Fatima Hasan , have you had it confirmed that your answer is officially correct?

15. Jan 2, 2018

No