A man pulls a 25kg sled a distance of 80 meters across a flat, snowy surface. He holds the handle of the sled at an angle of 30degrees with the ground. How much work does he do on the sled against the force of friction?(Assume the coefficient of sliding friction between the sled and the snow to be .1, and cos30=.87).
See previous post.
To find out how much work the man does on the sled against the force of friction, we need to calculate the force applied by the man first.
The force applied by the man can be determined using the equation:
Force = Mass * Acceleration
However, since the sled is being pulled on a flat surface, there is no acceleration. Therefore, the force applied by the man can be calculated using Newton's second law in the vertical direction:
Force = Mass * gravity * sinθ
Where:
Mass = 25 kg (mass of the sled)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
θ = 30 degrees
Now, let's calculate the force applied:
Force = 25 kg * 9.8 m/s^2 * sin(30 degrees)
= 25 kg * 9.8 m/s^2 * 0.5
= 122.5 N
The force of friction can be calculated using the equation:
Force of friction = Normal force * coefficient of sliding friction
Since the surface is flat and there is no vertical motion, the normal force is equal to the weight of the sled:
Normal force = Mass * gravity
Normal force = 25 kg * 9.8 m/s^2
= 245 N
Now, let's calculate the force of friction:
Force of friction = Normal force * coefficient of sliding friction
= 245 N * 0.1
= 24.5 N
The work done by the man against the force of friction can be calculated using the equation:
Work = Force * Distance * cosθ
Where:
Force = Force of friction = 24.5 N
Distance = 80 meters
θ = angle between force and direction of displacement = 30 degrees
Now, let's calculate the work done by the man:
Work = 24.5 N * 80 meters * cos(30 degrees)
= 24.5 N * 80 meters * 0.87
= 1701.6 Joules
Therefore, the man does approximately 1701.6 Joules of work on the sled against the force of friction.