A person lifts a 5.2 kg cement block a vertical distance 1.2 m and then carries the block horizontally a distance 7.3 m. Determine the work done by the person and by the force of gravity in this process.
Equals 3.14 over 8 over the power of 1/2.
To determine the work done by the person and by the force of gravity in lifting and carrying the cement block, we can use the equations for work:
Work = force x distance x cos(angle)
For the work done by the person, we need to calculate the work done in lifting the block vertically and the work done in carrying it horizontally. Let's calculate each separately:
1. Work done in lifting the block vertically:
First, we need to determine the force used to lift the block. The force exerted by the person can be calculated using Newton's second law:
Force = mass x acceleration
Since the block is being lifted vertically, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2. Plugging in the values:
Force = 5.2 kg x 9.8 m/s^2 = 50.96 N (rounded to two decimal places)
Now we can calculate the work done in lifting the block vertically:
Work = force x distance x cos(angle)
The distance is given as 1.2 m, and the angle between the force and the direction of motion (vertical direction) is 0 degrees since the force and the direction of motion are in the same direction. The cosine of 0 degrees is 1, so the equation becomes:
Work = 50.96 N x 1.2 m x 1 = 61.15 J (rounded to two decimal places)
Therefore, the work done by the person in lifting the block vertically is 61.15 Joules.
2. Work done in carrying the block horizontally:
Since the block is being carried horizontally, there is no vertical motion, and thus the force of gravity does not contribute to the work done horizontally. Therefore, the work done by the force of gravity in this process is zero.
Therefore, the total work done by the person is 61.15 Joules, and the work done by the force of gravity is 0 Joules.
M * g * 1.2 meters (by the person)
No work is done during the horizontal motion.
Work done by gravity is the same, with a minus sign.