A person lifts a 4.6 kg cement block a vertical distance of 1.43 m and then carries the block horizontally a distance of 10.50 m.
(a) How much work is done by the person in the process?
(b) How much work is done by gravity in the process?
To find the work done by the person and by gravity, we need to use the formulas for work and gravitational potential energy.
(a) The work done by the person can be calculated using the formula:
Work = Force × Distance
In this case, the person lifts the block vertically. Therefore, the force exerted by the person is equal to the weight of the block, which can be calculated using the formula:
Weight = mass × gravity
where gravity is the acceleration due to gravity, which is approximately 9.8 m/s².
So, the force exerted by the person is:
Force = mass × gravity = 4.6 kg × 9.8 m/s²
After finding the force, we can calculate the work done by the person by multiplying the force by the vertical distance:
Work = Force × Vertical Distance = (4.6 kg × 9.8 m/s²) × 1.43 m
(b) The work done by gravity can be calculated using the change in gravitational potential energy. Gravitational potential energy is given by the formula:
Gravitational Potential Energy = mass × gravity × height
In this case, the height is the vertical distance the block was lifted. So, the gravitational potential energy change is:
Gravitational Potential Energy Change = mass × gravity × Vertical Distance = 4.6 kg × 9.8 m/s² × 1.43 m
However, since the block was carried horizontally, the work done by gravity is zero in this direction. Therefore, the total work done by gravity in the process is zero.
To find the numerical values, simply substitute the given mass and distance into the equations mentioned above.