The efficiency of a pulley system is 47 percent.
The pulleys are used to raise a mass of 47 kg
to a height of 7.0 m.
The acceleration of gravity is 9.81 m/s
2
.
What force is exerted on the rope of the
pulley system if the rope is pulled for 28 m in
order to raise the mass to the required height?
Answer in units of N.
To find the force exerted on the rope of the pulley system, we can use the work and efficiency formulas.
First, let's calculate the work done by the pulley system. The work done is given by:
Work = force * distance
Given that the distance is 28 m and the force is what we want to find, we can rewrite the equation as:
Work = unknown force * 28 m
Next, let's calculate the work required to raise the mass to the required height. The work required is given by:
Work required = mass * gravity * height
Given that the mass is 47 kg, the acceleration due to gravity is 9.81 m/s^2, and the height is 7.0 m, we can substitute these values into the equation:
Work required = 47 kg * 9.81 m/s^2 * 7.0 m
Now, since the efficiency of the pulley system is given as 47%, we can define efficiency as the ratio of the useful work done to the total work done. In other words:
Efficiency = (Work done / Work required) * 100
We know that the efficiency is 47%, which can be written as 0.47. Rearranging the equation, we can solve for work done:
Work done = Efficiency * Work required
Substituting the given values, we get:
Work done = 0.47 * (47 kg * 9.81 m/s^2 * 7.0 m)
Now, we can set the work done equal to the unknown force multiplied by the distance:
unknown force * 28 m = 0.47 * (47 kg * 9.81 m/s^2 * 7.0 m)
Finally, we can solve for the unknown force:
unknown force = (0.47 * (47 kg * 9.81 m/s^2 * 7.0 m)) / 28 m
Evaluating this expression, we can find the force exerted on the rope of the pulley system.
To find the force exerted on the rope of the pulley system, we first need to calculate the work done in lifting the 47 kg mass to a height of 7.0 m.
The work done (W) is given by the formula:
W = force × distance
In this case, the distance is given as 28 m. To find the force, we can rearrange the formula as:
force = W / distance
Now, let's calculate the work done:
Work done (W) = mass × acceleration due to gravity × height
W = 47 kg × 9.81 m/s² × 7.0 m
W = 3237.75 J
Now, let's find the force exerted:
force = 3237.75 J / 28 m
force ≈ 115.62 N
Therefore, the force exerted on the rope of the pulley system is approximately 115.62 N.
work done by puller person
= F * 28
work done lifting weight
= .47 * F * 28 = 13.16 F
so
13.16 F = 47 * 9.81 * 7