Explanation:
To calculate the work done, we can use the formula:
Work = Force * Distance * cos(theta)
Given:
Mass of the body (m) = 20 kg
Resultant force (F) = 20 N
Angle with the vertical (theta) = 30 degrees
Distance (d) = 3 m
First, let's calculate the vertical component of the force:
Vertical component of the force = F * sin(theta)
= 20 N * sin(30 degrees)
= 10 N
Since the plane is smooth, there is no friction, and the only force acting on the body is the vertical component of the force. Therefore, the work done is given by:
Work = Force * Distance * cos(theta)
= 10 N * 3 m * cos(30 degrees)
= 10 N * 3 m * sqrt(3) / 2
= 15 sqrt(3) J (Joules)
Therefore, the work done on the body is approximately 25.98 Joules.
I hope this helps! Let me know if there's anything else I can assist you with.