Calculating Work Done on a Stubborn Sheep
How much work does a force of 30 N with an angle of 37° do on a stubborn sheep during displacement?
Given a constant horizontal force with a magnitude of 30 N and a direction 37° counterclockwise from the x-axis, what is the amount of work done by this force and what is the angle between the force and displacement during the sheep's movement?
Work Done and Angle Calculation
The amount of work done on the stubborn sheep is found using the equation W=F.d, with the angle between force and displacement taken as 0 degrees, given the force is applied in the direction of displacement. The actual value of work done depends on the displacement achieved.
Work done on an object by a force can be calculated using the equation:
W = F.d cos θ
Where:
W is work
F is the magnitude of the force
d is the displacement of the object
θ is the angle between the force and displacement vectors
In this case, the force and displacement are in the same direction, so the cosine of the angle between them is cos 0°, which is 1. Therefore, the work done is simply the product of the force and displacement.
To determine the amount of work done in nudging the stubborn sheep, we need to know the displacement achieved. Once the displacement (d) is known, you'll plug the values into the equation W = F.d.
Since the force is applied horizontally and counterclockwise from the X-axis, the angle θ between the force F and the displacement d is 37°. However, to calculate work, we are interested in the component of the force in the direction of displacement, i.e., along the horizontal. Thus, in reality, we must consider the angle as 0 degrees for work done as in this scenario, the work done is only due to the horizontal component of the force.