A rope applies a horizontal force of 208 N to pull a crate a distance of 1.91 m across the floor. A frictional force of 154 N opposes this motion.
(a) What is the work done by the force applied by the rope?
(b) What is the work done by the frictional force?
What is the total work done on the crate?
(a) 208 * 1.91 Joules
(b) -154 * 1.91 Joules
either add answers to a and b or do
(208-154)(1.91)
To find the work done by a force, we use the formula:
Work = Force × Distance × cos(θ)
where:
- Work is measured in joules (J)
- Force is measured in newtons (N)
- Distance is measured in meters (m)
- θ is the angle between the force and the direction of motion (if it's not given, we assume it to be 0°)
Now let's find the answers to the given questions:
(a) What is the work done by the force applied by the rope?
Given:
- Force applied by the rope = 208 N
- Distance = 1.91 m
Since the force is applied horizontally and the displacement is also horizontal, the angle θ between the force and the direction of motion is 0°. Therefore, cos(θ) = cos(0°) = 1.
So, the work done by the force applied by the rope is:
Work = Force × Distance × cos(θ)
Work = 208 N × 1.91 m × 1
Work = 397.28 J
(b) What is the work done by the frictional force?
Given:
- Frictional force = 154 N
- Distance = 1.91 m
Similar to the previous question, the force of friction acts in the opposite direction to the motion, so the angle θ between the force and the direction of motion is 180°. Therefore, cos(θ) = cos(180°) = -1.
So, the work done by the frictional force is:
Work = Force × Distance × cos(θ)
Work = 154 N × 1.91 m × (-1)
Work = -294.14 J
(c) What is the total work done on the crate?
To find the total work done on the crate, we can simply sum up the work done by both forces:
Total work = Work done by the force applied by the rope + Work done by the frictional force
Total work = 397.28 J + (-294.14 J)
Total work = 103.14 J
Therefore, the total work done on the crate is 103.14 Joules (J).