A gardener pushes a lawn roller through a distance of 20 m. If he applies a force of 20 N in a direction inclined at 60° to the ground, find the work done by the gardener on the lawn mover
The work done by the gardener is given by:
W = Fd cosθ
where F is the force applied by the gardener, d is the distance covered by the lawn roller, and θ is the angle between the force and the direction of motion.
In this case, F = 20 N, θ = 60°, and d = 20 m. Therefore, the work done by the gardener is:
W = 20 N x 20 m x cos60°
W = 200 J
Therefore, the gardener has done 200 Joules of work on the lawn roller.
To find the work done, we need to find the component of the force in the direction of displacement. Since the force is inclined at 60° to the ground, we can find the horizontal component of the force using the following formula:
Horizontal component of force = Force * cos(angle)
F_horizontal = 20 N * cos(60°)
Since cos(60°) = 1/2:
F_horizontal = 20 N * (1/2) = 10 N
Now that we have the horizontal component of the force, we can find the work done using the formula:
Work done = Force x Distance
W = F_horizontal * Distance
W = 10 N * 20 m
W = 200 J
The work done by the gardener on the lawn roller is 200 Joules.
To find the work done by the gardener on the lawn roller, we need to calculate the dot product of the applied force and the displacement.
Work (W) = Force (F) × Displacement (d) × cos(θ)
Where:
- Force (F) = 20 N
- Displacement (d) = 20 m
- Angle between the force and displacement (θ) = 60°
First, let's calculate the cosine of 60 degrees:
cos(60°) = 0.5
Now, we can use the formula to find the work done:
W = 20 N × 20 m × 0.5
W = 200 joules
Therefore, the gardener has done 200 joules of work on the lawn roller.
To find the work done by the gardener on the lawn roller, you need to know two things: the force applied and the displacement of the lawn roller.
In this case, the force applied by the gardener is 20 N and the distance covered by the lawn roller is 20 m. However, since the force is applied at an angle of 60° to the ground, you need to find the component of the force in the direction of the displacement. Let's calculate it step by step:
Step 1: Calculate the component of the force in the direction of displacement.
The component of the force in the direction of displacement is given by the formula:
Force (in the direction of displacement) = Force x Cosine(angle)
Force (in the direction of displacement) = 20 N x Cosine(60°)
Force (in the direction of displacement) = 20 N x 0.5
Force (in the direction of displacement) = 10 N
Step 2: Calculate the work done.
The work done is given by the formula:
Work done = Force x Distance
Work done = 10 N x 20 m
Work done = 200 Joules
Therefore, the gardener has done 200 Joules of work on the lawn roller.