What is the work done by the two forces together in moving an object a distance of d = 5 m as shown in the diagram? The magnitude of each force is 19 N.
Diagram:
(The two forces, F1 and F2, have the same magnitud but F1 is 45º over de the x axis, and F2 is 45º below de x axis. We are taking x axis as the line of distance, d.)
netforce=2*19cos45
work=netforce*distance
To find the work done by the two forces together in moving the object a distance of 5 m, we need to calculate the work done by each force and then add them together.
1. Calculate the work done by force F1:
Since force F1 is at an angle of 45º above the x-axis, we need to find the component of force F1 in the direction of the displacement, d.
The component of force F1 in the x-direction is given by:
Fx1 = F1 * cos(θ)
= 19 N * cos(45º)
= 19 N * (√2/2)
= 19 N * 0.7071
= 13.4359 N
The work done by force F1 is given by:
Work1 = Fx1 * d
= 13.4359 N * 5 m
= 67.179 N·m or 67.179 J
2. Calculate the work done by force F2:
Since force F2 is at an angle of 45º below the x-axis, we need to find the component of force F2 in the direction of the displacement, d.
The component of force F2 in the x-direction is given by:
Fx2 = F2 * cos(θ)
= 19 N * cos(45º)
= 19 N * (√2/2)
= 19 N * 0.7071
= 13.4359 N
The work done by force F2 is given by:
Work2 = Fx2 * d
= 13.4359 N * 5 m
= 67.179 N·m or 67.179 J
3. Calculate the total work done by the two forces together:
The total work done by the two forces together is the sum of Work1 and Work2:
Total work = Work1 + Work2
= 67.179 N·m + 67.179 N·m
= 134.358 N·m or 134.358 J
Therefore, the work done by the two forces together in moving the object a distance of 5 m is 134.358 N·m or 134.358 J.
To find the work done by the two forces together in moving the object a distance of 5 m, we need to calculate the work done by each force separately and then add them together.
The work done by a force can be calculated using the formula:
Work = Force x Distance x cos(theta)
Where:
- Force is the magnitude of the force
- Distance is the distance moved in the direction of the force
- theta is the angle between the force and the direction of motion
Let's calculate the work done by each force:
For force F1, the angle theta is 45 degrees above the x-axis. Since the force is acting parallel to the x-axis, the angle between the force and the direction of motion is 0 degrees.
So, the work done by F1 is:
Work1 = Force x Distance x cos(theta1)
= 19 N x 5 m x cos(0 degrees)
= 19 N x 5 m x 1
= 95 Joules
For force F2, the angle theta is 45 degrees below the x-axis. Since the force is acting parallel to the x-axis, the angle between the force and the direction of motion is 180 degrees.
So, the work done by F2 is:
Work2 = Force x Distance x cos(theta2)
= 19 N x 5 m x cos(180 degrees)
= 19 N x 5 m x (-1)
= -95 Joules
Now, to find the total work done by the two forces together, we sum up the works done by each force:
Total work = Work1 + Work2
= 95 Joules + (-95 Joules)
= 0 Joules
Therefore, the total work done by the two forces together in moving the object a distance of 5 m is 0 Joules.