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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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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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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
Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
5.0 5.0 (3 lesson ratings) (3)
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,
Eliminate a=T/5 and solve for T:
T=150/12=12.5 N