Dirk pushes on a packing box with a horizontal force of 67.0 N as he slides it along the floor. The average friction force acting on the box is 5.10 N. How much total work is done on the box in moving it 2.20 m along the floor?
To find the total work done on the box, we need to calculate the work done by the applied force and the work done by the friction force.
1. Work done by the applied force:
The work done by a constant force is given by the equation:
Work = Force × Distance × cos(θ), where θ is the angle between the force and the displacement.
In this case, the applied force is acting horizontally, so θ = 0°.
Work done by the applied force = 67.0 N × 2.20 m × cos(0°) = 67.0 N × 2.20 m × 1 = 147.4 J
2. Work done by the friction force:
The work done by a friction force can be calculated using the equation:
Work = Force × Distance × cos(θ), where θ is the angle between the force and the displacement.
The friction force acts in the opposite direction of the displacement, so θ = 180°.
Work done by the friction force = 5.10 N × 2.20 m × cos(180°) = 5.10 N × 2.20 m × (-1) = -11.22 J
3. Total work done on the box:
Total work done = Work done by the applied force + Work done by the friction force
Total work done = 147.4 J + (-11.22 J) = 136.18 J
Therefore, the total work done on the box in moving it 2.20 m along the floor is 136.18 J.
To find the total work done on the box, we need to calculate the work done by the applied force and the work done by the friction force separately, and then add them together.
The work done by a force is given by the equation:
Work = Force * Distance * cos(θ)
In this case, the applied force is 67.0 N and the distance is 2.20 m. The angle θ is 0 degrees since the force is applied horizontally.
Therefore, the work done by the applied force is:
Work_applied = 67.0 N * 2.20 m * cos(0°)
Since cos(0°) = 1, the above equation simplifies to:
Work_applied = 67.0 N * 2.20 m * 1 = 147.4 J
Next, let's calculate the work done by the friction force. The formula remains the same:
Work_friction = Force_friction * Distance * cos(θ)
The friction force is given as 5.10 N and the distance is 2.20 m. The angle θ is again 0 degrees.
Therefore, the work done by the friction force is:
Work_friction = 5.10 N * 2.20 m * cos(0°)
Since cos(0°) = 1, the above equation simplifies to:
Work_friction = 5.10 N * 2.20 m * 1 = 11.22 J
Finally, we can find the total work done on the box by adding the work done by the applied force and the work done by the friction force:
Total work = Work_applied + Work_friction
= 147.4 J + 11.22 J
= 158.62 J
Therefore, the total work done on the box in moving it 2.20 m along the floor is 158.62 Joules (J).