The force shown in the figure moves an object from x = 0 to x = 60 m, where the interval between vertical dashed lines is 20 m.
(a) How much work is done by the force?
(b) How much work is done by the force if the object moves from x = 20 to x = 60 m? (IN J)
You have to tell us how much the force is. Multiply it by the distance moved to get the work done.
a)0.45
To calculate the work done by a force, you need to multiply the force applied by the distance over which the force is applied. In this case, since the force is varying, we'll need to calculate the work done for each interval separately.
(a) To find the total work done by the force as the object moves from x = 0 to x = 60 m, we need to calculate the work done for each interval and then sum them up.
First, let's determine the force applied in each interval. Looking at the graph, we can see that the force is constant between each pair of vertical dashed lines.
From x = 0 to x = 20 m, the force is constant at 20 N.
From x = 20 to x = 40 m, the force is constant at 40 N.
From x = 40 to x = 60 m, the force is constant at 30 N.
Next, we'll calculate the work done in each interval and sum them up:
Work done in the first interval = Force x Distance = 20 N x 20 m = 400 J
Work done in the second interval = Force x Distance = 40 N x 20 m = 800 J
Work done in the third interval = Force x Distance = 30 N x 20 m = 600 J
Total work done by the force = 400 J + 800 J + 600 J = 1800 J
Therefore, the work done by the force as the object moves from x = 0 to x = 60 m is 1800 J.
(b) To determine the work done by the force if the object moves from x = 20 to x = 60 m, we need to calculate the work done for the interval from x = 20 m to x = 60 m.
From x = 20 to x = 40 m, the force is constant at 40 N.
From x = 40 to x = 60 m, the force is constant at 30 N.
The work done in this interval can be calculated as follows:
Work done in the interval = Force x Distance = (40 N x 20 m) + (30 N x 20 m) = 800 J + 600 J = 1400 J
Therefore, the work done by the force as the object moves from x = 20 to x = 60 m is 1400 J.
To calculate the work done by a force, we need to use the formula:
Work = Force x Distance x Cos(θ)
Where:
- Force is the magnitude of the force being exerted,
- Distance is the displacement covered by the object, and
- θ is the angle between the force vector and the direction of displacement.
From the given figure, we can see that the force being exerted is constant, as the graph is a straight line. Let's analyze the two given scenarios:
(a) When the object moves from x = 0 to x = 60 m:
The total distance covered by the object in this case is 60 m. To calculate the work done, we need to find the force and angle θ between the force and displacement. Since the force is constant, we can calculate the force by finding the change in y-coordinates between two points on the graph, and the angle θ is 0° degrees because the force and displacement are parallel.
- Force = Change in y-coordinates = 10 N - 0 N = 10 N
- Distance = 60 m
- θ = 0°
Now we can substitute these values into the work formula:
Work = Force x Distance x Cos(θ)
= 10 N x 60 m x Cos(0°)
= 10 N x 60 m x 1
= 600 J
Therefore, the work done by the force when the object moves from x = 0 to x = 60 m is 600 Joules (J).
(b) When the object moves from x = 20 to x = 60 m:
In this case, the distance covered by the object is 60 m - 20 m = 40 m. We need to find the force and θ again. The force is still constant, and the angle θ is still 0°, as the force and displacement are parallel.
- Force = Change in y-coordinates = 10 N - 10 N = 0 N
- Distance = 40 m
- θ = 0°
Now we substitute these values into the work formula:
Work = Force x Distance x Cos(θ)
= 0 N x 40 m x Cos(0°)
= 0
Therefore, the work done by the force when the object moves from x = 20 to x = 60 m is 0 Joules (J).