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1. A man of mass m = 80.0 kg hangs from a rope down into a hole. The rope goes over a massless pulley and is connected to a block of rock of mass M = 200 kg, which is lying on a frictionless horizontal surface. The distance between pulley and man is 5.00 m; between pulley and block 20.0 m.
a) What is the acceleration of the man (and rock)? How long does it take before the block crashes into the pulley, rips it off and everything plunges into the hole? The block and man start from rest.
b) Instead of just hanging there, the man decides to climb up the rope while everything is moving. Is it possible for him to get enough (constant) acceleration to get to the pulley and to safety, before the block hits the pulley? What is the acceleration of him and of the block in the case where he just makes it?
F=m*a ; Newtons Second Law.
m_1 = 200kg
m_2 = 80kg
distance between pulley and rock = 20m
distance between man and pulley = 5m
For a) I used the Newtons Second Law to make an equation relative to acceleration [ a=(m_2*g)/(m_1+_2) ] and got the answer 2,8m/s^2.
For a) to find the time from rocks start position to the pulley, I found the ewuation D=a*(t^2/2), which in the end turns out to be: t=sqrt(2D/a) which gives me 3,778 sec.
For task b) however, i can't figure out a smart way to find the relative time and acceleration that proves if he makes it or not. Tried it several times, but haven't found anything. This is what need help with. Thanks to all response on beforehand :)
1. A man of mass m = 80.0 kg hangs from a rope down into a hole. The rope goes over a massless pulley and is connected to a block of rock of mass M = 200 kg, which is lying on a frictionless horizontal surface. The distance between pulley and man is 5.00 m; between pulley and block 20.0 m.
a) What is the acceleration of the man (and rock)? How long does it take before the block crashes into the pulley, rips it off and everything plunges into the hole? The block and man start from rest.
b) Instead of just hanging there, the man decides to climb up the rope while everything is moving. Is it possible for him to get enough (constant) acceleration to get to the pulley and to safety, before the block hits the pulley? What is the acceleration of him and of the block in the case where he just makes it?
Homework Equations
F=m*a ; Newtons Second Law.
m_1 = 200kg
m_2 = 80kg
distance between pulley and rock = 20m
distance between man and pulley = 5m
The Attempt at a Solution
For a) I used the Newtons Second Law to make an equation relative to acceleration [ a=(m_2*g)/(m_1+_2) ] and got the answer 2,8m/s^2.
For a) to find the time from rocks start position to the pulley, I found the ewuation D=a*(t^2/2), which in the end turns out to be: t=sqrt(2D/a) which gives me 3,778 sec.
For task b) however, i can't figure out a smart way to find the relative time and acceleration that proves if he makes it or not. Tried it several times, but haven't found anything. This is what need help with. Thanks to all response on beforehand :)