A machine has a velocity ratio of 6 and is 80% efficient. What effort would be needed to lift of 300N with the aid of this machine
To find the effort needed to lift 300N with the aid of this machine, we need to use the formulas for efficiency and velocity ratio.
Efficiency (η) is given by the formula:
η = (output work / input work) × 100%
Velocity Ratio (VR) is given by the formula:
VR = distance moved by effort / distance moved by load
Given that the velocity ratio is 6, we can write this as:
6 = distance moved by effort / distance moved by load
So, distance moved by effort = 6 × distance moved by load
Now, if the load is 300N, the distance moved by load (d) can be calculated using the formula:
Work done by load = force × distance moved by load
Therefore, input work (W_in) is given by:
W_in = 300N × d
Now, if the efficiency is 80%, we can convert it to a decimal by dividing by 100:
Efficiency (η) = 0.8
Using the Efficiency formula mentioned above, the output work (W_out) is given by:
W_out = η × W_in
So,
W_in = 300N × d
W_out = 0.8 × W_in
We can rearrange the equation W_out = 0.8 × W_in to solve for W_in:
W_in = W_out / 0.8
Substituting W_in = 300N × d, we get:
300N × d = W_out / 0.8
Now, using the Velocity Ratio formula, we know that distance moved by effort (d_effort) is 6 times distance moved by load (d_load):
d_effort = 6 × d_load
Substituting d_load = d and d_effort = 6d_load, we get:
6d_load = d
Now, we can substitute 6d_load for d in the equation 300N × d = W_out / 0.8:
300N × (6d_load) = W_out / 0.8
Rearranging this equation to solve for W_out, we get:
W_out = 300N × (6d_load) × 0.8
Further simplifying this equation, we have:
W_out = 1440N × d_load
Therefore, the effort needed to lift the 300N load with the aid of this machine is 1440N.