3)-A 9-kg block is held by a pulley system shown in fig. What force must the person exert in the following cases: a) to hold the block at rest. b) to lower it at 2m/s. c) to raise it with an acceleration of 0.5 m/s2? Ignore the mass of small pulley.
what figure?
i cant post it but its a man who is pulling a mass and the mass is hanging from a pulley and he is in a higher position not on the floor
Bruh
To find the force that the person must exert in each case, let's analyze the forces acting on the block.
First, let's clarify some given information:
- The mass of the block is 9 kg.
- The system includes a pulley, but we can ignore its mass.
- The figure is not provided, so I cannot refer to it.
Now, let's break down the forces for each case:
a) To hold the block at rest:
In this case, we assume that the block is not moving. Therefore, the net force acting on the block must be zero.
The forces acting on the block are:
1. The force of gravity pulling the block downward, given by F_gravity = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²).
2. The force provided by the person, which we need to find.
Since the block is at rest, the force provided by the person must exactly balance the force of gravity. Therefore, the force provided by the person is equal in magnitude but opposite in direction to the force of gravity, so it is F_gravity = 9 kg * 9.8 m/s² = 88.2 N.
b) To lower it at 2 m/s:
In this case, the block is being lowered at a constant velocity of 2 m/s. That means the net force acting on the block must be zero, just like in the previous case.
Again, the forces acting on the block are:
1. The force of gravity pulling the block downward, as before.
2. The force provided by the person, which we need to find.
Since the block is moving at a constant velocity, the force provided by the person must balance the force of gravity, just like in the previous case. Therefore, the force provided by the person is also F_gravity = 88.2 N.
c) To raise it with an acceleration of 0.5 m/s²:
In this case, the block is being raised with an upward acceleration of 0.5 m/s². That means the net force acting on the block is not zero, since there is an additional force required to create the acceleration.
The forces acting on the block are:
1. The force of gravity pulling the block downward, as before.
2. The force provided by the person, which we need to find.
To solve for the force provided by the person, we need to consider the net force equation:
Net force = mass * acceleration
The net force is the force provided by the person minus the force of gravity, so we have:
Force provided by the person - Force of gravity = mass * acceleration
Substituting the given values, we have:
Force provided by the person - 88.2 N = 9 kg * 0.5 m/s²
Simplifying the equation:
Force provided by the person = 88.2 N + 4.5 N
Force provided by the person = 92.7 N
Therefore, in order to raise the block with an acceleration of 0.5 m/s², the person must exert a force of approximately 92.7 N.