A block and tackle consisting of 5 pulleys is used to raise a load of 400N through a height of 10m. If the work done against friction is 1000joules. Calculate
A. The work done by the effort
B. The efficiency of the system
C. The effort applied
A. The work done by the effort can be calculated using the work formula:
Work = Force * Distance
Given:
Force (effort) = ?
Distance = 10m
Work = ?
Since no information is given about the force applied, we cannot directly calculate the work done by the effort. We need additional information in order to solve this part of the question.
B. The efficiency of the system can be calculated using the formula:
Efficiency (%) = (Useful Work Output / Total Work Input) * 100
Given:
Total Work Input = 1000 joules (work done against friction)
Useful Work Output = 400N * 10m (work done to raise the load)
Efficiency (%) = (400N * 10m / 1000 joules) * 100
Efficiency (%) = 40%
C. The effort applied cannot be calculated without additional information about the force applied.
To solve this problem, we can use the principles of work and energy.
A. The work done by the effort:
The work done by the effort can be calculated using the equation:
Work done by effort = Total work done - Work done against friction
Given that the total work done is the product of the force applied (effort) and the distance moved, we can calculate the total work done:
Total work done = Force × Distance
= 400N × 10m
= 4000 joules
Substituting the values into the equation for work done by effort:
Work done by effort = 4000 joules - 1000 joules
= 3000 joules
Therefore, the work done by the effort is 3000 joules.
B. The efficiency of the system:
The efficiency of a system is the ratio of useful output energy (work done by the effort) to the input energy (total work done). It can be calculated using the equation:
Efficiency = (Useful output energy / Input energy) × 100%
Substituting the values of useful output energy (work done by effort) and input energy (total work done):
Efficiency = (3000 joules / 4000 joules) × 100%
= (0.75) × 100%
= 75%
Therefore, the efficiency of the system is 75%.
C. The effort applied:
The effort applied can be calculated using the formula:
Effort = (Load × Distance) / Number of supporting strands
In this case, the load is 400N, the distance is 10m, and there are 5 supporting strands (pulleys).
Effort = (400N × 10m) / 5
= 800N
Therefore, the effort applied is 800N.
To solve these questions, we'll need to use the formulas related to work and mechanical advantage. Let's start with part A:
A. The work done by the effort:
We can calculate the work done by multiplying the force exerted by the distance covered. The formula is:
Work = Force × Distance
In this case, the work done against friction is given as 1000 Joules, so the total work done by the effort (W_effort) can be calculated as:
W_effort = Work against friction + Work done to raise the load
= 1000 J + Work done to raise the load
Now, let's find the work done to raise the load using the formula:
Work done to raise the load = Force × Distance
Here, the force is the weight of the load, which can be calculated as:
Force = Mass × Gravity
Given that the load is 400 N and the height is 10 m, we can calculate the work done to raise the load:
Work done to raise the load = 400 N × 10 m
Now, substitute the value of the work done to raise the load into the equation for W_effort:
W_effort = 1000 J + (400 N × 10 m)
Calculate the value of W_effort.
B. The efficiency of the system:
Efficiency is defined as the ratio of useful work output to the total work input. In this case, useful work output is the work done against friction, and total work input is the work done by the effort. So the efficiency (E) can be calculated as:
E = (Useful work output / Total work input) × 100%
Use the values we calculated in part A to find the efficiency.
C. The effort applied:
The effort applied is the force applied by the person operating the block and tackle system. In this case, it is the force required to overcome the load and any friction. We can calculate it using the formula:
Effort = Load / Mechanical Advantage
To find the mechanical advantage, we can use the formula:
Mechanical Advantage = Total number of ropes supporting the load
Since the block and tackle system consists of 5 pulleys, the mechanical advantage is 5.
Now, calculate the effort.