Exciting Physics Problem: Work Done by Forces
What is the work done when a box is moved across a smooth floor by forces at angles?
Given: A box is moved 20 m across a smooth floor by a force making a downward angle with the floor. There is effectively a 10 N force acting parallel to the floor in the direction of motion and a 5 N force acting perpendicular to the floor. What is the work done?
Answer:
The work done is 100 Joules.
From the given question, the work done by the forces in moving the box can be calculated using the formula:
W = Fx * d * cosФ + Fy * d * cosα
Where:
- W = Work done
- Fx = Force acting parallel to the floor
- d = Distance moved by the box (20 m)
- Ф = Angle the parallel force makes with the floor
- Fy = Force acting perpendicular to the floor
- α = Angle the perpendicular force makes with the floor
Given values: Fx = 10 N, d = 20 m, Fy = 5 N, Ф = 0°, α = 90°
Substitute the values into the formula:
W = 10 * 20 * cos(0°) + 5 * 20 * cos(90°)
W = 10 * 20 * 1 + 0
W = 200
Therefore, the work done by the forces in moving the box is 100 Joules. It is important to note that the work done by the perpendicular force is zero in this case.