No worries, let's just focus on finding the correct answers for the questions!

[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, v_A?

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

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

a) 4 K_A
b) 2 K_A
c) K_A
d) K_A/2
e) K_A/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, x_A?

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

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

a) 8 F_A
b) 4 F_A
c) 2 F_A
d) F_A/2
e) F_A/4
f) F_A/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 k_A is 4k_B. If the work for both is equal, then F*d_A = F*d_B, and since k_A = 4k_B, 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!

 

[Tanya Sharma]

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, v_A?

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

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

a) 4 K_A
b) 2 K_A
c) K_A
d) K_A/2
e) K_A/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, x_A?

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

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

a) 8 F_A
b) 4 F_A
c) 2 F_A
d) F_A/2
e) F_A/4
f) F_A/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 k_A is 4k_B. If the work for both is equal, then F*d_A = F*d_B, and since k_A = 4k_B, 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!

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

It states W_net = 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 ?

 

[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.)

 

[BMcC]

So in 1. for B, it's 1/2 mv² = 4*F*d?

 

[Tanya Sharma]

So in 1. for B, it's 1/2 mv² = 4*F*d?

Yes..that is right .

 

[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 v_B not 4 times larger than v_A?

 

[nil1996]

you should take squareroots on both sides

 

[Tanya Sharma]

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 v_B not 4 times larger than v_A?

No...This means v_B² is equal to four times v_A²

 

[BMcC]

Oh damn. So vB = 2*vA?

 

[Tanya Sharma]

Yes ...

 

[nil1996]

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

 

[BMcC]

So 1. is b)!

Now onto the next ones...

 

[nil1996]

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

 

[Tanya Sharma]

So 1. is b)!

Now onto the next ones...

Correct.

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

So what is the answer according to you ?

 

[BMcC]

I am utterly confused

 

[Tanya Sharma]

I am utterly confused

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

Let nil1996 answer my question .

 

[nil1996]

Correct.
So what is the answer according to you ?

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

 

[Tanya Sharma]

block B is moving at a velocity 2V_a and block A is moving at speed V_a
So the relative velocity is V_a

That is simply wrong understanding.

Please read question carefully...Here relative means in comparision to .The question doesn't ask about relative velocity .

 

[nil1996]

That is simply wrong understanding.

Please read question carefully...Here relative means in comparision to .The question doesn't ask about relative velocity .

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?"
The answer would be 2m/s.

I think the problems is similar too.

 

[Tanya Sharma]

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?"
The answer would be 2m/s.

I think the problems is similar too.

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.

 

[nil1996]

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.

Where is the question saying find the relation between the two velocities ?

 

[Tanya Sharma]

Where is the question saying find the relation between the two velocities ?

Common sense...

 

[nil1996]

Common sense...

OK then let the discussion continue with next problem.You are taking the question roughly.

 

[Tanya Sharma]

BMcC...What is the answer to Q.2 ?

 

[berkeman]

Thread closed temporarily for Moderation...

 

[Mark44]

From the OP: What is the velocity of block B, relative to that of block A, V_A?

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

No, it's wrong. From the answers given it is clear that "relative to" means what multiple of V_A is V_B? Here, "relative to" DOES NOT mean the difference of the two velocities.

That is simply wrong understanding.

Please read question carefully...Here relative means in comparision to .The question doesn't ask about relative velocity .

Right. And again, "relative to" and "in comparison to" mean what multiple.

Where is the question saying find the relation between the two velocities ?

From the original problem statement, part of which I quoted at the top of this post. Also, from the given possible answers, it is clear that they're talking about multiples, not differences.

I am reopening this thread, taking it out of moderation.

nil1996, do not persist in taking this thread off track.

 

[nil1996]

From the OP: What is the velocity of block B, relative to that of block A, V_A?


No, it's wrong. From the answers given it is clear that "relative to" means what multiple of V_A is V_B? Here, "relative to" DOES NOT mean the difference of the two velocities.

Right. And again, "relative to" and "in comparison to" mean what multiple.


From the original problem statement, part of which I quoted at the top of this post. Also, from the given possible answers, it is clear that they're talking about multiples, not differences.

I am reopening this thread, taking it out of moderation.

nil1996, do not persist in taking this thread off track.

I am sorry for that.I realized i was taking word to word meaning.Sorry BmcC for confusing you.And last sorry Tanya Sharma for taking a long useless argument.