Please, help me solve this problem.
A block and tackle consisting of 4 pulleys is used to raise a load of 300N through a distance of 5m. If the work done against friction is 750J, calculate;
a) the work done by the effort
b) the efficiency of the machine
c) the effort applied
To solve this problem, we need to use the formulas related to work and efficiency. Let's break down each part:
a) Work done by the effort:
The work done by the effort is equal to the work done against friction plus the work done to lift the load. We are given that the work done against friction is 750J. To calculate the work done to lift the load, we need to use the formula:
Work = Force * Distance
The force is equal to the weight of the load, which is given as 300N and the distance is given as 5m. So, the work done to lift the load is:
Work = 300N * 5m = 1500J
Finally, we can calculate the work done by the effort:
Work done by the effort = Work done to lift the load + Work done against friction
= 1500J + 750J
= 2250J
Therefore, the work done by the effort is 2250J.
b) Efficiency of the machine:
The efficiency of a machine is defined as the ratio of useful work output to the total work input. In this case, the useful work output is the work done to lift the load, which is 1500J, and the total work input is the work done by the effort, which is 2250J. To calculate the efficiency, we use the formula:
Efficiency = (Useful work output / Total work input) * 100
Substituting the values:
Efficiency = (1500J / 2250J) * 100
= 0.6667 * 100
= 66.67%
Therefore, the efficiency of the machine is 66.67%.
c) Effort applied:
The effort applied refers to the force exerted by the person or machine operating the block and tackle system. In this case, the effort applied can be calculated using the formula:
Effort applied = Load / Mechanical advantage
The mechanical advantage of a block and tackle system is equal to the number of ropes supporting the load. In this case, we are given that there are 4 pulleys in the system, so the mechanical advantage is 4. Substituting the values:
Effort applied = 300N / 4
= 75N
Therefore, the effort applied is 75N.