Search 80,000+ tutors
Ask a question
0 0

What's the downward acceleration?

Two masses are connected by a light cord which is looped over a light frictionless pulley. If one mass is 3.0 kg and the second mass is 5.0 kg, what's the downward acceleration of the heavier mass? Assume air resistance is negligible.
Answer: 2.5 m/s^2
Tutors, please sign in to answer this question.

2 Answers

A quick way: Treat two masses as a whole system. The net downward force is (m1-m2)g, where m1 = 5 kg, and m2 = 3 kg.
Apply Newton's second law to the whole system:
(m1-m2)g = (m1+m2)a
Solve for a,
a = (m1-m2)g/(m1+m2) = (5-3)g/(5+3) = 2.45 m/sec2 <==Answer
Apply Newton's 2nd law to each mass:
For the 3.0-kg mass, which moves up,
3a=T-3g, where T is the tension in the cord.
For the 5.0-kg mass, which moves down,
Eliminate T and get
a=g/4=9.8/4=2.45 m/s².