A block and tackle of 6 pulley is used to raise a load of 30N steadily through a height of 3m. If the work done against friction is 100J and the total work done by the effort is 500J. Calculate:
a. The work done to raise the load
b. The efficiency of the system
c. The applied effort
work output is load weight * height raised = 30 N * 3 m = 90 Joules
work wasted in friction = 100 Joules
work input = 90 + 100 = 190 Joules
efficiency = 100 * work output / work input = 100 (90/190) = 47.4 %
If applied effort is the force in it is 1/6 * 190/3 = 10.6 Newtons
To solve this problem, we need to use the following formulas:
a. Work = Force x Distance
b. Efficiency = (Work Output / Work Input) x 100%
c. Applied Effort = Load / Mechanical Advantage
Given:
Load = 30N
Height = 3m
Work against friction = 100J
Total work done by the effort = 500J
Step 1: Calculate the work done to raise the load.
Using the formula, Work = Force x Distance, we have:
Work = Load x Height
Work = 30N x 3m
Work = 90J
Therefore, the work done to raise the load is 90J.
Step 2: Calculate the efficiency of the system.
Using the formula, Efficiency = (Work Output / Work Input) x 100%, we have:
Efficiency = (Work done to raise the load / Total work done by the effort) x 100%
Efficiency = (90J / 500J) x 100%
Efficiency = 18%
Therefore, the efficiency of the system is 18%.
Step 3: Calculate the applied effort.
Using the formula, Applied Effort = Load / Mechanical Advantage, we have:
Mechanical Advantage = Number of pulleys = 6
Applied Effort = 30N / 6
Applied Effort = 5N
Therefore, the applied effort is 5N.
To solve this problem, we can use the concepts of work and mechanical advantage.
a. The work done to raise the load:
Work is given by the formula: Work = Force × Distance
In this case, the work done against friction is given as 100J. The total work done by the effort is given as 500J.
The total work done equals the work done to raise the load plus the work done against friction. So we can set up the following equation:
500J = work done to raise the load + 100J
To find the work done to raise the load, we can rearrange the equation:
Work done to raise the load = 500J - 100J
Work done to raise the load = 400J
Therefore, the work done to raise the load is 400J.
b. The efficiency of the system:
Efficiency is given by the formula: Efficiency = (useful work output / total work input) × 100%
The useful work output in this case is the work done to raise the load, which is 400J. The total work input is the work done by the effort, which is 500J.
Efficiency = (400J / 500J) × 100%
Efficiency = 0.8 × 100%
Efficiency = 80%
Therefore, the efficiency of the system is 80%.
c. The applied effort:
To find the applied effort, we need to use the concept of mechanical advantage. The mechanical advantage is the ratio of the load force to the effort force.
The load force is 30N and is equal to the weight of the load being raised.
The mechanical advantage can be calculated using the formula: Mechanical Advantage = Load Force / Effort Force
The mechanical advantage of a block and tackle system with 6 pulleys is given by the formula: Mechanical Advantage = 2^n, where n is the number of pulleys.
In this case, we have 6 pulleys, so the mechanical advantage is: Mechanical Advantage = 2^6 = 64
To calculate the applied effort, we can set up the following equation:
Load Force / Effort Force = Mechanical Advantage
30N / Effort Force = 64
To find the Effort Force, we can rearrange the equation:
Effort Force = Load Force / Mechanical Advantage
Effort Force = 30N / 64
Effort Force = 0.46875N
Therefore, the applied effort is approximately 0.47N.