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What's the tension?

Two masses 5.0 and 7.0 kg are originally at rest on a frictionless surface. The masses are connected by a light cord. A second cord is attached to the 7.0 kg mass and pulled with a horizontal force of 30 N. What's the tension in the cord that connects the two masses?

Answer: 12.5 N

 
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2 Answers

Step 1.Treat two masses as a whole system, and apply Newton's second law:
F = (m1+m2)a, where m1 = 5 kg, and m2 = 7 kg
30 = (5+7)a
a = 30/12 = 2.5 m/s^2
 
Step 2. Apply Newton's second law to m1.
T = m1a = 5*2.5 = 12.5 N <==Answer
Apply Newton's 2nd law to both masses. For the 5.0-kg mass,
 
5a=T,  where T is the tension in the cord.
 
For the 7.0-kg mass,
 
7a=-T+30.
 
Eliminate a=T/5 and solve for T:
 
7(T/5)=-T+30
(12/5)T=30
T=150/12=12.5 N
 

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