A machine with velocity ratio 5 was used to raise a load of 1.2kg mass through a height of 10m. If the work done is 800j, find the useful workout, Efficiency and mechanical advantage of the machine
To find the useful work output, efficiency, and mechanical advantage of the machine, we can use the following formulas:
1. Useful work output (W_out):
W_out = work done on the load (W_load)
2. Efficiency (η):
η = (W_out / W_in) * 100%
3. Mechanical advantage (MA):
MA = load / effort = W_load / W_effort
Now, let's calculate the values step by step:
Step 1: Calculate the work done on the load (W_load):
W_load = mass * acceleration due to gravity * height
W_load = 1.2 kg * 9.8 m/s² * 10 m
W_load = 117.6 J
Step 2: Calculate the useful work output (W_out):
W_out = W_load
W_out = 117.6 J
Step 3: Calculate the efficiency (η):
η = (W_out / W_in) * 100%
Since the problem does not provide the value of the input work (W_in), we cannot calculate the efficiency without this information.
Step 4: Calculate the mechanical advantage (MA):
MA = W_load / W_effort
Since the velocity ratio is given as 5, we can relate it to the mechanical advantage as:
MA = velocity ratio / MA_ratio (where MA_ratio = 1)
MA = 5 / 1
MA = 5
Summary:
- Useful work output (W_out) = 117.6 J
- Efficiency (η) cannot be calculated without the input work (W_in)
- Mechanical advantage (MA) = 5