A man is sitting in a bosun's chair that dangles from a massless, frictionless pulley and back down to the mans's hand. The combined mass of man and chair is 100 kg.
With what force magnitude (N) must the man pull on the rope if he is to rise with a constant velocity? ..with an upward acceleration of 1.29 m/s2?
If the rope extends to the ground and is pulled by a co-worker, with what force magnitude must the co-worker pull for the man to rise with a constant velocity? .. and with an upward acceleration of 1.29 m/s2?
Draw the vector diagram.
Tension = mg+ma -handforce on the chair side.
On the rope side, Tension=handforce.
So solving, Tension= handforce
so handforce=(mg+ma) 1/2
but how do you determine what 'a' is?
.. when i try to solve for 'a'.. i reach a deadend with having to solve for T also.
hmm.. is it 0?
For constatn velocity F is 490N; for upward acceleration of 1.29 m/s2 it is
554.9N
For coworker F is 980N to rise with constant velocity and 1109N to rise with acceleration of 1.29.
You know that when he is moving with a constant velocity, a=0 , when he is moving with acceleration, a=1.29 m/s^2 . Now plug in the numbers you have into the equations and you will come up with the answers you provided.
To determine the force magnitude required for the man to rise with a constant velocity or with an upward acceleration of 1.29 m/s^2, we need to consider the forces acting on the system.
1. Constant velocity:
When the man is rising with a constant velocity, the force of gravity pulling him downward is balanced by the tension in the rope. Since there is no net force, the force magnitude required for the man to rise with a constant velocity is equal to the weight of the man and the chair.
Force magnitude (constant velocity) = Weight of the man + Weight of the chair = (mass of man + mass of chair) x acceleration due to gravity
2. Upward acceleration of 1.29 m/s^2:
When the man is rising with an upward acceleration, in addition to the force of gravity, there needs to be an additional force to overcome the inertia of the system. In this case, the force magnitude required will be the sum of the force that balances the weight and the force to accelerate upwards.
Force magnitude (upward acceleration) = Weight of the man + Weight of the chair + (mass of man + mass of chair) x acceleration
To solve for 'a' (the acceleration), we can rearrange the equations as follows:
For constant velocity:
Force magnitude = (mass of man + mass of chair) x acceleration due to gravity
For upward acceleration:
Force magnitude = (mass of man + mass of chair) x (acceleration due to gravity + acceleration)
Since the question does not provide any information about 'a', we cannot determine the value of 'a' without additional information or assumptions.
To draw the vector diagram, you can represent the forces acting on the system as arrows. Use the length of each arrow to represent the magnitude of the force, and the direction of the arrow to indicate the direction of the force. In this case, you would have arrows representing the weight of the man and chair, the tension in the rope, and the force applied by the man or coworker.