A force of 12 N is applied to the handle of a screwdriver being used to pry off the lid of a paint can. As the force moves through a distance 0.3 m, the screwdriver does 3.2 J of work on the lid. What is the efficiency of the screwdriver? Show your work.
efficiency = [3.2 / (12 * 0.3)] * 100%
To find the efficiency of the screwdriver, we need to compare the work done by the screwdriver to the work input (the energy transferred to it).
The work done by the screwdriver can be calculated using the formula:
Work = Force x Distance
Given:
Force = 12 N
Distance = 0.3 m
Work = 3.2 J
Substituting the given values into the formula, we have:
3.2 J = 12 N x 0.3 m
Now, let's calculate the work input (the energy transferred to the screwdriver) using the same formula:
Work(input) = Force x Distance
Given:
Force = 12 N
Distance = 0.3 m
Work(input) = 12 N x 0.3 m
Now we can calculate the efficiency using the formula:
Efficiency = (Work / Work(input)) x 100
Substituting the values into the formula:
Efficiency = (3.2 J / (12 N x 0.3 m)) x 100
Simplifying, we get:
Efficiency = (3.2 J / 3.6 J) x 100
Efficiency = 88.89%
Therefore, the efficiency of the screwdriver is approximately 88.89%.
To find the efficiency of the screwdriver, we need to calculate the work input and work output and then divide the work output by the work input.
Work input (WI) is calculated by multiplying the applied force (F) by the distance the force is applied (d):
WI = F * d
Given:
Force (F) = 12 N
Distance (d) = 0.3 m
WI = 12 N * 0.3 m
WI = 3.6 J
The work output (WO) is given as 3.2 J.
Efficiency (E) is calculated by dividing the work output by the work input and multiplying by 100 to express the result as a percentage:
E = (WO / WI) * 100
E = (3.2 J / 3.6 J) * 100
E = 0.8889 * 100
E = 88.89%
Therefore, the efficiency of the screwdriver is approximately 88.89%.