A block moves up a 30° incline under the action of certain forces, three of which are shown at the right. F1 is horizontal and of magnitude 40 N. F2 is normal to the plane and of magnitude 20 N. F3 is parallel to the plane and magnitude 30 N. (a) Determine the work done by each force as the block (and point of application of each force) moves 80 cm up the incline. (b) What is the work done by the gravity? (c) Find the total work done on the block excluding the work of frictional force
Not knowing if F3 is up the plane or down, it is hard to say. I suppos F1 is pushing up, but again it is unclear.
A block moves up a 30° incline under the action of certain forces, three of which
are shown at the right. F₁ is horizontal and of magnitude 40 N. F₂ is normal to the
plane and of magnitude 20 N. F3 is parallel to the plane and magnitude
30 N. (a) Determine the work done by each force as the block (and point of
application of each force) moves 80 cm up the incline. (b) What is the work done by
the gravity? (c) Find the total work done on the block excluding the work of frictional
force.
To determine the work done by each force as the block moves up the incline, we need to use the formula:
Work = Force * Distance * cos(theta)
where theta is the angle between the force and the direction of motion.
(a) Work done by F1:
F1 is horizontal, so the angle between F1 and the direction of motion is 90 degrees. Therefore, cos(90) = 0.
Work1 = F1 * Distance * cos(90) = 40 N * 0.8 m * 0 = 0 J
Work done by F2:
F2 is normal to the plane, so it is perpendicular to the direction of motion. Therefore, cos(theta) = 0.
Work2 = F2 * Distance * cos(theta) = 20 N * 0.8 m * 0 = 0 J
Work done by F3:
F3 is parallel to the plane, so the angle between F3 and the direction of motion is 0 degrees. Therefore, cos(0) = 1.
Work3 = F3 * Distance * cos(0) = 30 N * 0.8 m * 1 = 24 J
(b) The work done by gravity can be calculated using the formula:
Work_gravity = Force_gravity * Distance * cos(theta_gravity)
where Force_gravity is the weight of the block and theta_gravity is the angle between the force of gravity and the direction of motion.
The weight of the block can be calculated using the formula:
Force_gravity = mass * acceleration_due_to_gravity
Given that the mass of the block is not provided, we cannot calculate the exact value for the work done by gravity.
(c) To find the total work done on the block excluding the work of the frictional force, we simply need to add up the work done by each force.
Total work done = Work1 + Work2 + Work3 = 0 J + 0 J + 24 J = 24 J