# Tension on a string between two objects on a friction less surface [closed]

I just need my work checked here. Please let me know if I am correct. I had this problem in one of my test in which I did not get full credits. I am re-doing this(hopefully correctly this time) just for my own peace of mind and understanding.

Problem statement: The force shown of 6.4N pulls horizontally on the 1.5kg block that is connected by a string to the second block of mass 0.93 kg. Assuming a smooth friction less surface find acceleration of the blocks and tension in the string. If there is friction, what happens to the tension in the string? (increase, decrease, stay the same? show your logic)

The system and my free body diagram:

Given: m1 = 1.5 kg

m2 = .93 kg

F = 6.4 N

Total Mass = m1+m2 = 2.43 kg

Finding acceleration:

F = ma

F = (m1 + m2)a

6.4N = (2.43kg)a

## a = 2.63 m/s2

Finding Tension:

m1 = (1.5 kg)(9.81m/s2)= 14.7 N

m2 = (0.93 kg)(9.81m/s2)= 9.11 N

## T = (m1+m2) + 6.4 N = 14.7 N + 9.11 N + 6.4 N = 30.4 N

If there is friction, the tension would increase. As the friction increases the force that pulls the two objects would have to be greater therefore increasing the tension.(The way I thought about is if there was friction, the blocks would require more force to move, since we already established that the net force is 6.4, the tension would have to increase to balance the frictional force.)

I just wanted to make sure that I at least had the correct concept down. Any, criticism and suggestions are welcome.

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## closed as off-topic by Chris White, Brandon Enright, Valter Moretti, John Rennie, Waffle's Crazy PeanutMar 6 '14 at 9:32

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As the blocks are moving horizontally, the gravity and normal forces cancel each other. So your logic about finding the tension is faulty. You should use Newtons second law on each separate block. To find the tension you could suffice with the last one.

If there is friction you could add the friction force to the equation, and think about what this would do to the acceleration, and net force per block

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So, I should use the acceleration I found for the system instead of using gravity for the calculation? T = (m_1+m_2)a + F_Net Would this be correct? – MakkaCha Mar 5 '14 at 21:18
To much for the frictionless surface. T=m_2*a only. With the friction T=m_2*a+F_frict,noting that a would differ from the acceleration on the frictionless floor. – KvdLingen Mar 5 '14 at 21:28

The tension in the string has nothing to do with gravity. Just consider the forces acting in the horizontal direction for each mass separatedly.

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I haven't checked the arithmetic, but the method to calculate the acceleration is right.

The easiest way (to my mind) to find the tension (T) in the string is to apply F=ma to the smaller mass block. Hope fully if you do that, you will also find that (T-6.4) will also accelerate the larger mass at the required rate as well.

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