Force pushing two gliders on an air track.

[kevinius]

A 6N force pushes to gliders along an air track. The 200 g spring between the gliders is compressed. How much force does the spring exert on (a) glider A and (b) glider B?

Mass of Glider A = 400 g
Mass of Glider B = 600 g

I just want to verify that I solved this problem correctly. If I've made some mistake, please let me know.

3. I first set up my free body diagram for all three objects. Because the gliders are on the air track, friction is negligible. I also know that I don't have to consider forces in the y-direction because there is no acceleration there. Because both gliders are moving to the right, their acceleration is the same.

Find acceleration:
6N/(0.4 kg) = 15 m/s^2

Based on my free body diagram of the spring, the summation of the forces in the x-direction is:

F spring = F (s on B) - F (s on A) = m(s) * a

= F (s on B) - F (s on A) = (0.20 kg)(15 m/s^2)

= F (s on B) - F (s on A) = 3N

F (s on A) is equal to the F (A on s) = 6N

F (s on B) = 3N + 6N = 9N

 

[PhanthomJay]

A 6N force pushes to gliders along an air track. The 200 g spring between the gliders is compressed. How much force does the spring exert on (a) glider A and (b) glider B?

Mass of Glider A = 400 g
Mass of Glider B = 600 g

I just want to verify that I solved this problem correctly. If I've made some mistake, please let me know.




3. I first set up my free body diagram for all three objects. Because the gliders are on the air track, friction is negligible. I also know that I don't have to consider forces in the y-direction because there is no acceleration there. Because both gliders are moving to the right, their acceleration is the same.

Find acceleration:
6N/(0.4 kg) = 15 m/s^2

This is not the FBD of the first block. More than one force acts on it. The 6 N force acts on the entire blocks and spring system. Solve for the acceleration of the system, then look at a FBD of each block. Be sure of the direction of the forces.

 

[kevinius]

Okay. So the acceleration of the total system is: 6N/(0.4 kg + 0.2 kg + (0.6 kg) = 5 m/s^2.

Since the 6N force applies to the entire system, when I do my FBD of glider A, would it have the 6N force to the right and the force of the spring on A to the left?

 

[PhanthomJay]

Okay. So the acceleration of the total system is: 6N/(0.4 kg + 0.2 kg + (0.6 kg) = 5 m/s^2.

Since the 6N force applies to the entire system, when I do my FBD of glider A, would it have the 6N force to the right and the force of the spring on A to the left?

yes, that is correct. Compressive or pushing forces always act toward the object on which they act.

 

[kevinius]

The sum of the forces for Glider A = 6N - F (s on A) = 2N. This leaves F(s on A) equal to 4N. I do know that this force is pointing to the left.

The spring only has two forces acting upon it: the force of B exerted on the spring and the force of A exerted on the spring. The sum of forces of the spring = F (A on s) - F (B on s) = 1N.

The F (A on s) is equal to the F (s on A), thus:

4N - F (B on s) = 1N ===> -F (B on s) = -3N ===> F (B on s) = 3N.

F (B on s) and F (s on B) are the same as well, but I know that the force of the spring on Glider B must be greater than the force on Glider A because the difference in mass.

What is it that I'm missing?

 

[PhanthomJay]

Your answers are correct, but your logic is not. If both A and B accelerate at the same rate, it is not the spring force that must be greater on the heavier mass, but rather, use Newton 2 to determine which net force must be greater.

 

[kevinius]

The problem is asking what force the spring is exerting on Glider A and Glider B. The spring force on A = -4N. The spring force on B = 3N.

 

[PhanthomJay]

The problem is asking what force the spring is exerting on Glider A and Glider B. The spring force on A = -4N. The spring force on B = 3N.

Yes, correct.

 

[kevinius]

Wow...it was that simple. I appreciate you nudging me in the right direction!