To push a 25.0kg crate up a frictionless surface incline angled at 25 degrees to the horizontal, a worker exerts a force of magnitude 209N parallel to the incline. As the crate slides 1.50m, how much work is done on they crate by (a) the worker's applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) what is the total work done?
How do I get started?
work: 209*1.5 joules total
normal force=mgSin25
gravitational force on crate=mg
workers force=209
To find the work done on the crate by different forces, we need to use the formula:
Work = Force * Distance * cos(theta)
Where:
- Work is the amount of work done on the crate
- Force is the magnitude of the force applied
- Distance is the distance over which the force is applied
- theta is the angle between the force and the direction of motion
Now, let's solve each part of the question step by step:
(a) Work done by the worker's applied force:
The worker exerts a force of magnitude 209N parallel to the incline. Since the crate slides up the incline, the angle between the force and the direction of motion is 0 degrees (cos(0) = 1). We can substitute these values into the formula:
Work = Force * Distance * cos(theta)
Work (worker's force) = 209N * 1.50m * cos(0)
(b) Work done by the gravitational force:
The gravitational force acting on the crate can be calculated using the formula:
Force (gravity) = mass * acceleration due to gravity
Force (gravity) = 25.0kg * 9.8m/s^2
Since the crate is moving up the incline, the angle between the gravitational force and the direction of motion is 180 degrees (cos(180) = -1). We can substitute these values into the formula:
Work = Force * Distance * cos(theta)
Work (gravity) = -Force (gravity) * 1.50m * cos(180)
(c) Work done by the normal force:
The normal force exerted by the incline on the crate is perpendicular to the direction of motion. Therefore, the angle between the normal force and the direction of motion is 90 degrees (cos(90) = 0). We can substitute these values into the formula:
Work = Force * Distance * cos(theta)
Work (normal force) = 0 * 1.50m * cos(90)
(d) Total work done:
To find the total work done, we need to sum up the work done by each force:
Total work done = Work (worker's force) + Work (gravity) + Work (normal force)