Using Fig. 4.28 as an example, how much applied force would the man need to have to pull the block (weight or output force = 500 N) if the rope he is holding is 7 m long and the rope on the pulley is 2 m long? (Hint, the pulley is a simple machine)
To find the amount of applied force that the man needs to pull the block, we can use the principle of a simple machine, specifically the principle of a pulley.
First, let's understand how a pulley works. A pulley is a simple machine that consists of a wheel with a grooved rim and a rope running along the groove. It is used to change the direction of a force or to multiply the effort force applied.
In this case, we have a block with a weight or output force of 500 N. The pulley is connected to the block by a rope, which is 7 m long. The other end of the rope is held by the man. Another rope is attached to the pulley and is 2 m long.
When the man applies a force to the rope, it generates tension in the rope, which in turn affects the block. The forces involved in the system are the applied force (F_applied), the tension in the rope (T), and the weight or output force (F_weight) of the block.
We can apply Newton's second law of motion to the pulley system. When the system is in equilibrium, the forces acting on it will balance each other out. In this case, the tension in the rope will be the same on both sides, and therefore the magnitude of the tension can be considered the same.
To find the applied force, we need to solve for the tension in the rope. We can use the following equation:
T = F_weight / (number of supporting ropes)
In this case, the number of supporting ropes is 2 because there are two ropes attached to the pulley.
T = 500 N / 2
T = 250 N
Now that we know the tension in the rope is 250 N, we can find the applied force by considering the mechanical advantage of the pulley system. The mechanical advantage is the ratio of the output force to the input force.
In this case, since the block weight or output force is 500 N and there are two supporting ropes, the mechanical advantage is:
Mechanical Advantage = Output Force / Input Force
Mechanical Advantage = 500 N / F_applied
Given that the length of the rope on the pulley is 2 m and the length of the rope held by the man is 7 m, we can find the mechanical advantage using the ratio of their lengths:
Mechanical Advantage = Length of pulley rope / Length of rope held by the man
Mechanical Advantage = 2 m / 7 m
Mechanical Advantage = 0.2857
Setting the mechanical advantage equal to the mechanical advantage equation above, we can solve for the applied force:
0.2857 = 500 N / F_applied
To find F_applied, we can rearrange the equation:
F_applied = 500 N / 0.2857
F_applied ≈ 1747.82 N
Therefore, the man would need to apply an approximate force of 1747.82 N to pull the block in this scenario.