A block of mass
m = 5.0 kg
is pulled along a rough horizontal surface by a rope as sketched in the figure below. ( rope is at a 30 degree angle from the horizontal) The tension in the rope is 50 N, and the coefficient of kinetic friction between the block and the surface is
μK = 0.35.
(a) If the block travels a distance of 6.0 m along the surface, what is the work done by the rope?
259.8J
(b) Find the work done by friction on the block.
I tried to use Workk= coefficient of friction x mass x g x displacement
= .35(5kg) (9.8) (6m)= 102.9 and then negative because it is in the opposite direction of the work done by the rope. but this is not correct.
Then I tried the same formula and added cos(angle)
Workk= - (coefficient of friction) (mass) (g) (displacement) (cos(angle))
=(.35) (5) (9.8) (6) (cos 150)
= -89.1
I am not sure what else to try.
You didn't give me the collect answer
To correctly calculate the work done by friction on the block, you need to consider the angle between the force of friction and the displacement of the block. In this case, the force of friction acts in the opposite direction to the displacement of the block, so you need to use the angle of 180 degrees.
The formula to calculate work done is:
Work = force × displacement × cos(angle)
Since the force of friction is acting in the opposite direction, the angle is 180 degrees, and the work done by friction can be calculated as:
Work_friction = force_friction × displacement × cos(180 degrees)
The force of friction can be calculated using the formula:
force_friction = coefficient_of_friction × normal_force
The normal force, in this case, is the weight of the block, which is the mass of the block multiplied by the acceleration due to gravity (9.8 m/s^2).
Substituting the given values into the equations:
force_friction = μ × m × g
force_friction = (0.35) × (5 kg) × (9.8 m/s^2)
force_friction = 17.15 N
Work_friction = force_friction × displacement × cos(180 degrees)
Work_friction = (17.15 N) × (6 m) × cos(180 degrees)
Since cos(180 degrees) = -1, the equation simplifies to:
Work_friction = -17.15 N × 6 m × (-1)
Work_friction = 103 N·m or 103 J (rounded to the nearest whole number)
So the correct answer for the work done by friction on the block is approximately 103 J, not -89.1 J as you calculated earlier.