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).
Ws = m*g = 25kg *9.8N/kg = 245 N. = Wt of sled.
Fs = 245N @ 0o. = Force of sled
Fp = 245*sin(0) = 0 = Force parallel to
surface.
Fv = 245*cos(0) = 245 N. = Force perpendicular to surface.
Fn = Fap*cos30-Fp-0.1(Fv-Fap*sin30) = ma
0.87Fap-0-0.1(245-0.5Fap) = 25*0 = 0
0.87Fap - 24.5 + 0.05Fap = 0
0.92Fap - 24.5 = 0
0.92Fap = 24.5
Fap = 24.5 / 0.92 = 26.6 N. = Force applied.
Work = Fap*cos30 * d
Work = 26.6*cos30 * 80 = 1851.4 Joules.
To calculate the work done on the sled against the force of friction, we need to consider the formula for work:
Work = Force x Distance x cos(θ)
In this case, the force we are concerned with is the force of friction. The formula for friction force is:
Friction Force = μ * Normal Force
where μ is the coefficient of sliding friction and the normal force is the force perpendicular to the surface. When an object is at an angle to the ground, the formula for the normal force is:
Normal Force = Weight x cos(θ)
Given that the sled has a mass of 25 kg, the weight can be calculated as:
Weight = mass x acceleration due to gravity
= 25 kg x 9.8 m/s^2
= 245 N
Now, let's calculate the normal force:
Normal Force = 245 N x cos(30°)
= 245 N x 0.87
= 213.15 N
Substituting the values into the friction force formula:
Friction Force = 0.1 x 213.15 N
= 21.315 N
Finally, we can calculate the work done on the sled:
Work = Friction Force x Distance x cos(θ)
To find the work, we need to use the value of the distance given, which is 80 meters, and the angle θ given, which is 30 degrees:
Work = 21.315 N x 80 m x cos(30°)
= 21.315 N x 80 m x 0.87
= 1466.64 J
Therefore, the man does 1466.64 Joules of work on the sled against the force of friction.