A machine raises a load of 600N through a height of 1.5m when an effort of 100N moves a total distance of 20m.(a) calculate the work done in raising the load.(b) what is the mechanical advantage of the machine?(c) calculate the efficiency of the machine.
a) Fd = 600*1.5
b) 6:1
c) Fd ideal/Fd actual
600* 1.5 =900 /200 =4.5 *100 =450
(a) To calculate the work done in raising the load, we can use the formula: work = force x distance.
In this case, the force is the load being raised, which is 600N, and the distance is the height being raised, which is 1.5m.
So, the work done in raising the load is:
Work = force x distance
Work = 600N x 1.5m
Work = 900 Joules
(b) The mechanical advantage of a machine can be calculated using the formula: mechanical advantage = load / effort.
In this case, the load is 600N and the effort is 100N.
So, the mechanical advantage of the machine is:
Mechanical advantage = load / effort
Mechanical advantage = 600N / 100N
Mechanical advantage = 6
(c) Efficiency can be calculated as the ratio of useful work performed by the machine to the total energy input. The total energy input is the product of effort force and distance moved.
Efficiency = (useful work / total energy input) x 100%
The useful work is the work done in raising the load, which is 900 Joules (calculated in part a).
The total energy input is the product of effort force and distance moved, which is given as 100N x 20m = 2000 Joules.
So, the efficiency of the machine is:
Efficiency = (900 Joules / 2000 Joules) x 100%
Efficiency = 45%
To calculate the answers to these questions, we need to use the formulas and definitions related to work, mechanical advantage, and efficiency.
(a) To calculate the work done in raising the load, we use the formula:
Work = Force × Distance
In this case, the force is the load being raised, which is 600N, and the distance is the height the load is raised, which is 1.5m. Therefore, we can calculate:
Work = 600N × 1.5m = 900 Joules
So, the work done in raising the load is 900 Joules.
(b) To calculate the mechanical advantage (MA) of the machine, we use the formula:
MA = Output Force / Input Force
In this case, the output force is the load being raised, which is 600N, and the input force is the effort, which is 100N. Therefore, we can calculate:
MA = 600N / 100N = 6
So, the mechanical advantage of the machine is 6.
(c) To calculate the efficiency of the machine, we use the formula:
Efficiency = (Useful Output Energy / Input Energy) × 100
In this case, the useful output energy is the work done in raising the load, which is 900 Joules, and the input energy is the work done by the effort, which is the force applied (100N) multiplied by the distance covered (20m). Therefore, we can calculate:
Input Energy = 100N × 20m = 2000 Joules
Efficiency = (900 Joules / 2000 Joules) × 100 = 45%
So, the efficiency of the machine is 45%.