A person pushes a 10 kg crate 5 m up a 29 degree incline with an 80 N force parallel to the incline. The fricitonal force is 20 N.
Find the work done:
a) by the person
b) by gravity
c) by friction
a. Work = F*d = 80 * 5 = 400 J.
b. h = 5*sin29 = 2.424 m.
Work = F*h = mg*h = 98*2.424 = 237.6 J.
c. Work = 20 * 5 = 100 J.
To find the work done, we will use the formula: Work = Force * Distance * cos(angle).
a) The work done by the person can be calculated using the force exerted by the person parallel to the incline. The force exerted by the person is 80 N. The distance moved by the crate is 5 m. The angle between the force and the direction of motion is 29°. Therefore, the work done by the person is:
Work = 80 N * 5 m * cos(29°)
b) The work done by gravity can be calculated using the weight of the crate and the vertical distance it moves. The weight of the crate is given by the formula: Weight = mass * gravitational acceleration. Given that the crate has a mass of 10 kg and the gravitational acceleration is approximately 9.8 m/s^2, the weight of the crate is:
Weight = 10 kg * 9.8 m/s^2 = 98 N
Since the crate is moved up a vertical distance of 5 m, the work done by gravity is:
Work = -98 N * 5 m * cos(180°)
Here, the negative sign indicates that the force of gravity is acting in the opposite direction of the displacement.
c) The work done by friction can be calculated using the force of friction and the distance the crate moves. The force of friction is given as 20 N. The distance moved by the crate is 5 m. Since the angle between the force of friction and the displacement is 180°, the work done by friction is:
Work = -20 N * 5 m * cos(180°)
Again, the negative sign indicates that the force of friction is acting in the opposite direction of the displacement.
To find the work done in each scenario, we can use the formula: Work = Force * Distance * Cos(angle)
a) Work done by the person:
The force applied by the person is 80 N, and the distance covered is 5 m. The angle between the force and the displacement is the incline angle, which is 29 degrees. So the work done by the person can be calculated as:
Work = 80 N * 5 m * Cos(29 degrees)
b) Work done by gravity:
Gravity acts vertically downward, perpendicular to the direction of motion. Therefore, the work done by gravity is zero because the displacement and force are perpendicular to each other.
Work = 0
c) Work done by friction:
The frictional force is 20 N, and the distance covered is also 5 m. The angle between the frictional force and the displacement is 180 degrees since they are in opposite directions. So the work done by friction can be calculated as:
Work = -20 N * 5 m * Cos(180 degrees)
Note: The negative sign indicates that the frictional force opposes the motion.
It's important to remember that the cosine of 180 degrees is -1, which is why we have a negative sign in the formula.
By plugging in the respective values into the equations, you can calculate the work done in each scenario.