Two masses are connected by a light string passing over a light, frictionless pulley?

Question

The m1 = 5.35 kg object is released from rest at a point 4.00 m above the floor, where the m2 = 2.70 kg object rests.


a)Determine the speed of each object when the two pass each other.______m/s

b) Determine the speed of each object at the moment the 5.35 kg mass hits the floor.______m/s

c)How much higher does the 2.70 kg mass travel after the 5.35 kg mass hits the floor?_______m

need help on this one guys. thanks alot.

Answer 1

This is called an Atwood machine

T-m1g=m1a

m2g-T=m2a

Eliminating T and solving for the acceleration we get

a=(5.35-2.7)/(5.35+2.7)*9.8=3.23 m/s^2

s=1/2at^2
v=at
so v=sqrt(2as). In this case s=2, the halfway point

so v=3.59 m/s

when the 5.35 weight hits the floor the velocity is

sqrt(2*4*3.23)=5.08 m/s

s=-1/2gt^2+5.08t+5. differentiate and find the maximum height of the weight. You should get 1.32 m more.