A 8.72 kg particle moves from the origin to position C , having coordinates x = 2.04 m and y = 2.04 m as shown in Figure 1. A particle moving in a horizontal plane from the origin to position C experiences a friction force with constant magnitude 2.32 N. Calculate the work that you must do to slide the particle at constant speed against the friction force as the particle moves along the diagonal path.
you must balance the friction by applying an equal and opposite force, or 2.32N
work = force * distance = 2.32*2.04√2
To calculate the work done to slide the particle at constant speed against the friction force, we can use the formula:
Work = Force * Distance * cos(theta)
In this case, the force is the friction force, the distance is the displacement of the particle along the diagonal path, and theta is the angle between the displacement vector and the direction of the force.
To find the displacement along the diagonal path, we can use the Pythagorean theorem:
Displacement = sqrt((x^2) + (y^2))
where x and y are the coordinates of position C.
Given that x = 2.04 m and y = 2.04 m, the displacement can be calculated as follows:
Displacement = sqrt((2.04^2) + (2.04^2)) = sqrt(8.3216 + 8.3216) = sqrt(16.6432) = 4.08 m
The angle theta can be calculated as the arctan of y/x:
theta = arctan(y/x) = arctan(2.04/2.04) = arctan(1) = 45 degrees
Now we have all the values we need to calculate the work:
Work = 2.32 N * 4.08 m * cos(45 degrees)
To calculate the cosine of 45 degrees, we can use the trigonometric identity that cos(45 degrees) = sqrt(2)/2:
Work = 2.32 N * 4.08 m * (sqrt(2)/2)
Simplifying the expression:
Work = 4.32 N * 4.08 m * sqrt(2)
Work = 35.276 J (rounded to three significant figures)
Therefore, the work that must be done to slide the particle at constant speed against the friction force along the diagonal path is approximately 35.276 J.