A machine has a velocity ratio of 6 and is 80% efficient. What effort would be needed to lift a load of 300N with the aid of the machine?
First, we need to determine the ideal mechanical advantage (IMA) of the machine, which is calculated using the velocity ratio formula:
IMA = output distance ÷ input distance
Since this formula is not given, we can use the definition of velocity ratio:
velocity ratio = output velocity ÷ input velocity
and substitute output distance for output velocity and input distance for input velocity.
velocity ratio = output distance ÷ input distance
6 = output distance ÷ input distance
Therefore, the IMA of the machine is 6.
Next, we can use the efficiency formula:
efficiency = (output work ÷ input work) x 100%
Rearranging the formula:
output work = (efficiency ÷ 100%) x input work
We know that the input work is equal to the work done by the effort, which can be calculated as:
work = force x distance
where force is the effort required to lift the load and distance is the distance the effort moves.
We don't know the distance the effort moves yet, but we can solve for the force using the IMA formula:
IMA = load ÷ effort
6 = 300N ÷ effort
effort = 300N ÷ 6
effort = 50N
Now we can use the work formula to find the distance the effort moves:
work = force x distance
input work = effort x distance
output work = load x distance
Substituting the values we know:
(80% ÷ 100%) x (50N x distance) = 300N x distance
0.8 x 50N x distance = 300N x distance
40N x distance = 300N x distance
Simplifying:
40N = 300N
distance = 7.5m
Therefore, the effort required to lift a load of 300N with the aid of the machine is 50N.
To find the effort needed to lift a load with the aid of a machine, we can use the formula:
Effort = (Load / Velocity Ratio) / Efficiency
Given:
Load = 300N
Velocity Ratio = 6
Efficiency = 80%
First, let's convert the efficiency from a percentage to a decimal by dividing it by 100:
Efficiency = 80% / 100 = 0.8
Now we can substitute the values into the formula:
Effort = (300N / 6) / 0.8
Simplifying this expression, we get:
Effort = 50N / 0.8
Finally, we can calculate the effort:
Effort = 62.5N
Therefore, the effort needed to lift the 300N load with the aid of the machine would be 62.5N.