a person lifts a 4.3 kg centimeter block a vertical distance of 1.10m. and then carries the block horizontally a distance of 10.0m.
How much work is done by the person?
How much work is done by gravity?
To determine the work done by the person and by gravity, we need to understand the concept of work and the relevant formulas.
Work is defined as the product of the force applied to an object and the distance over which the force is applied. Mathematically, work (W) is calculated using the formula:
W = F * d * cos(theta),
where F is the force applied, d is the distance over which the force is applied, and theta is the angle between the force and displacement vectors. In this case, since the block is lifted vertically and then carried horizontally, theta is 90 degrees for the lifting and 0 degrees for the horizontal movement.
The work done by the person is equal to the force applied by the person multiplied by the distance over which the force is applied. Since the block is lifted vertically against the force of gravity, the force exerted by the person is equal to the weight of the block. The weight of an object is given by the formula:
Weight = mass * g,
where mass is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
Therefore, the work done by the person is given by:
W_person = weight * vertical distance.
In this case, the vertical distance is 1.10 m, and the weight of the block can be calculated as:
Weight = mass * g = 4.3 kg * 9.8 m/s^2.
Once you have the weight of the block, you can calculate the work done by the person using the formula mentioned above.
To calculate the work done by gravity, note that when the block is lifted vertically, gravity does negative work, as its force is in the opposite direction of the displacement. The work done by gravity can be given as:
W_gravity = -weight * vertical distance.
After the block is lifted, no work is done by gravity during the horizontal movement, as the displacement is perpendicular to the force of gravity.
Therefore, the work done by gravity is only during the lifting phase, and it can be calculated using the formula mentioned above.
Plug in the given values into these formulas, and you will be able to calculate the work done by the person and by gravity.