A force of 100N pulls a box of weight 200N along a smooth horizontal surface makes 45(degree) to the floor .
Calculate the work done by the force.
A- in moving the box a distance of 25m along the horizontal.
B- against gravity.
C- against normal force.
Horizontal component = 100 cos 45 = 70.7
Work done by moving 25 m = 70.7*25 Joules
THE MOTION IS HORIZONTAL!!!
It does not move in the direction of gravity, thus zero
It likewise does not move in the direction of the normal force --> zero
This is a trick question intended to remind you that the work done is force IN THE DIRECTION OF MOTION times distance moved (also of course in the direction of motion)
To calculate the work done by a force, we use the formula:
Work = Force × Displacement × cos(θ)
where
- Force is the magnitude of the force applied,
- Displacement is the distance moved in the direction of the force, and
- θ is the angle between the force and the direction of displacement.
A) To calculate the work done in moving the box a distance of 25m along the horizontal, the force and the displacement are in the same direction, so θ = 0 degrees.
Work = Force × Displacement × cos(θ)
= 100N × 25m × cos(0)
= 100N × 25m × 1
= 2500 Joules
Therefore, the work done by the force in moving the box horizontally is 2500 Joules.
B) To calculate the work done against gravity, we need to determine the vertical component of the force. The vertical component can be found by multiplying the force by the sine of the angle θ.
Vertical Component of Force = Force × sin(θ)
= 100N × sin(45 degrees)
= 100N × 0.707
= 70.7N
Since the displacement is along the horizontal direction, there is no displacement in the vertical direction. Therefore, the work done against gravity is zero, as there is no vertical displacement.
C) The normal force acts perpendicular to the surface and has no component along the direction of displacement. Therefore, the work done against the normal force is also zero, as there is no displacement in the direction of the normal force.
In summary:
A) The work done by the force in moving the box horizontally is 2500 Joules.
B) The work done against gravity is zero.
C) The work done against the normal force is zero.