A block of mass 2.50 kg is pushed 2.80 m along a frictionless horizontal table by a constant 12.0 N force directed 25.0° below the horizontal.
(a) Determine the work done by the applied force.
J
(b) Determine the work done by the normal force exerted by the table.
J
(c) Determine the work done by the force of gravity.
J
(d) Determine the work done by the net force on the block.
J
Forces that are not applied in the direction of movement does no work.
The movement is horizontal.
a. Work = F*d = 12*cos25 * 2.8 = 30.5 J.
12*cos25 = Hor. component of applied force.
b. No work done.
c. No work done.
d. Same as a.
To determine the work done in each case, we need to use the formula for work:
Work = Force * Distance * cos(theta)
where Force is the applied force, Distance is the distance moved, and theta is the angle between the applied force and the direction of motion.
Let's calculate the work done in each case:
(a) Work done by the applied force:
Given: Force = 12.0 N, Distance = 2.80 m, theta = 25.0°
Using the formula, we have:
Work = 12.0 N * 2.80 m * cos(25.0°)
Work = 12.0 N * 2.80 m * 0.9063
Work ≈ 30.15 J
(b) Work done by the normal force exerted by the table:
In this case, the normal force is perpendicular to the direction of motion, so the angle theta is 90°. Therefore, cos(theta) = cos(90°) = 0.
Work = Force * Distance * cos(theta)
Work = 0
The work done by the normal force is zero because it does not contribute to the displacement of the object.
(c) Work done by the force of gravity:
The force of gravity acts vertically downwards, and the displacement is horizontal, so the angle theta is 90°. Therefore, cos(theta) = cos(90°) = 0.
Work = Force * Distance * cos(theta)
Work = 0
The work done by the force of gravity is also zero because it acts in a different direction from the displacement.
(d) Work done by the net force on the block:
The net force is the vector sum of the applied force and the force of gravity. Since the force of gravity does no work, we only need to consider the work done by the applied force.
Work done by the net force = Work done by the applied force = 30.15 J