# Springs (4 Multiple choice)

1. Oct 25, 2013

### BMcC

1. Two blocks of equal mass are each pushed (from rest) along a frictionless surface a distance d. The force applied to block B is four times that applied to block A. What is the velocity of block B, relative to that of block A, vA?

a) 4 vA
b) 2 vA
c) vA
d) vA/2
e) vA/4

2. What is the kinetic energy of block B relative to that of block A, KA?

a) 4 KA
b) 2 KA
c) KA
d) KA/2
e) KA/4

3. The same work is done compressing spring A or spring B from their equilibrium lengths. The spring constant of spring A is four times that of spring B. How much is spring B compressed relative to spring A, xA?

a) 8 xA
b) 4 xA
c) 2 xA
d) xA/2
e) xA/4
f) xA/8

4. What is the maximum force applied to spring B relative to that applied to spring A, FA?

a) 8 FA
b) 4 FA
c) 2 FA
d) FA/2
e) FA/4
f) FA/8

For 1. I figure that pushing B with 4 times the force would make it accelerate 4 times as fast, thus making the final velocity 4 times as fast as the velocity of block A if they both start at rest. So I chose a)

For 2. I figure that since the velocity of B is 4 times larger than the velocity of A, then the KE = 1/2 m*v2 would make the KE of B 4 times larger than the KE of A, so I chose a) again.

For 3. I figure that kA is 4kB. If the work for both is equal, then F*dA = F*dB, and since kA = 4kB, then B is compressed 4 times as much, so I chose b). I am unsure about this one.

For 4. I'm kind of confused...

Any help at all would be appreciated!

2. Oct 25, 2013

### Tanya Sharma

First consider Q.1) .Your answer and reasoning both are incorrect .Do you know Work Kinetic Energy Theorem ?

It states Wnet = ΔKE i.e net work done by all the external forces is equal to the change in the kinetic energy of the body .

Just Apply it .What do you get ?

3. Oct 25, 2013

### nil1996

You should not go on your logic. Write equations of motion and then you should understand how many problems are wrong!!!(first is wrong and i think others too are wrong.)

4. Oct 25, 2013

### BMcC

So in 1. for B, it's 1/2 mv2 = 4*F*d?

5. Oct 25, 2013

### Tanya Sharma

Yes..that is right .

6. Oct 25, 2013

### BMcC

So I work that out for B and get v2 = (8*F*d)/m.

I work it out for A and get v2 = (2*F*d)/m

So is vB not 4 times larger than vA?

7. Oct 25, 2013

### nil1996

you should take squareroots on both sides

8. Oct 25, 2013

### Tanya Sharma

No...This means vB2 is equal to four times vA2

9. Oct 25, 2013

### BMcC

Oh damn. So vB = 2*vA?

10. Oct 25, 2013

### Tanya Sharma

Yes ...

11. Oct 25, 2013

### nil1996

that's right
So what is the correct option of 1

12. Oct 25, 2013

### BMcC

So 1. is b)!

Now onto the next ones...

13. Oct 25, 2013

### nil1996

No,thats wrong.
see what is asked "What is the velocity of block B, relative to that of block A"

14. Oct 25, 2013

### Tanya Sharma

Correct.

So what is the answer according to you ?

15. Oct 25, 2013

### BMcC

I am utterly confused

16. Oct 25, 2013

### Tanya Sharma

No need to get confused ..Just carry on with the next part..

Let nil1996 answer my question .

17. Oct 25, 2013

### nil1996

block B is moving at a velocity 2Va and block A is moving at speed Va
So the relative velocity is Va . isn't it right??

18. Oct 25, 2013

### Tanya Sharma

That is simply wrong understanding.

19. Oct 25, 2013

### nil1996

If i say you are moving at 4 m/s and i at 2m/s in same direction and ask "what is your velocity relative to me?"

I think the problems is similar too.

20. Oct 25, 2013

### Tanya Sharma

Where is it mentioned that the two blocks are moving in the same direction ?

The question is asking for the relation between the two velocities ,not relative velocity.