Ayesha exerts a force of 186 N on a lever to raise a 2.70 × 103-N object to a height of 29.0 cm. If the
efficiency of the lever is 83.3 percent, how far does Ayesha move her end of the lever?
To find the distance Ayesha moves her end of the lever, we can use the formula for the efficiency of a lever:
Efficiency = (Output force / Input force) * 100
In this case, the output force is the weight of the object, which is 2.70 × 103 N, and the input force is the force Ayesha exerts on the lever, which is 186 N. We can rearrange the formula to solve for the output force:
Output force = (Efficiency / 100) * Input force
Now, we can substitute the given values into the formula:
Output force = (83.3 / 100) * 186 N
Output force = 0.833 * 186 N
Output force ≈ 154.638 N
The output force is equal to the weight of the object, so we can equate it to the weight formula:
Weight = mass * acceleration due to gravity
The weight of the object can be calculated by dividing the weight by the acceleration due to gravity, which is approximately 9.8 m/s²:
Weight = mass * 9.8 m/s²
Now, we can rearrange the formula to solve for the mass:
mass = Weight / 9.8 m/s²
Substituting the given value into the formula:
mass = 2.70 × 103 N / 9.8 m/s²
mass ≈ 275.51 kg
Given that the height the object is raised is 29.0 cm, we can convert it into meters:
height = 29.0 cm / 100 cm/m
height = 0.29 m
The work done on the object is equal to the force multiplied by the distance:
Work = Force * Distance
We can rearrange the formula to solve for the distance:
Distance = Work / Force
Substituting the given values into the formula:
Distance = (output force * height) / input force
Distance = (154.638 N * 0.29 m) / 186 N
Distance ≈ 0.240 m
Therefore, Ayesha moves her end of the lever approximately 0.240 meters.