An object is placed on an inclined plane which forms an angle B = 18º with the horizontal. An external force F of magnitude 14.3 N is applied to the object. The force F acts in a direction which forms an angle A = 62º with the horizontal. As a result of the force F, the object moves a distance of 0.8 m along the inclined plane. What work was done by the source of force F?
To find the work done by the source of force F, we can use the formula:
Work = Force * Distance * cos(theta)
Where:
- Work is the work done by the force F.
- Force is the magnitude of the force F.
- Distance is the distance over which the force F acts.
- theta is the angle between the force and the direction of motion.
Given:
- Force F = 14.3 N
- Distance = 0.8 m
- theta = 62º
First, we need to find the effective force acting along the direction of motion (i.e., parallel to the inclined plane). This can be calculated by finding the component of force F that is parallel to the inclined plane:
Force_parallel = Force * sin(theta)
Substituting the given values:
Force_parallel = 14.3 N * sin(62º)
Next, we need to find the angle between the direction of motion and the horizontal. This angle is the difference between the angle of the inclined plane (18º) and the angle of the applied force (62º):
Angle_difference = 18º - 62º
Now, we can find the final angle (theta_final) between the force and the direction of motion by subtracting the angle difference from 90º:
theta_final = 90º - Angle_difference
Substituting the given values:
theta_final = 90º - (18º - 62º)
Now, we can calculate the work done by the force F:
Work = Force_parallel * Distance * cos(theta_final)
Substituting the calculated values:
Work = (14.3 N * sin(62º)) * 0.8 m * cos(theta_final)
Finally, evaluate this equation to find the work done by the source of force F.