What's the tension?

Question

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

 

Answer 1

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

Answer 2

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