A crate with a total mass of 18.0 kg is pulled by a person along the floor at a constant speed by a rope. The rope is inclined at 20 degree above the horizontal, and the crate moves 20.0 m on a horizontal surface. The coefficient of kinetic friction between the floor and the crate is 0.50
And the questions are as follows:
a. Draw a free body diagram for the crate (solved)
b. What is the tension in the rope?
c. How much work is done on the crate by the rope?
d. What is the energy lost due to friction?
Wt. of crate=m*g=18kg * 9.8N/kg=176.4 N.
Fv = 176.4*cos0 = 176.4 N. = Force perpendicular to the surface.
Fk = u*Fv = 0.5 * 176.4 = 88.2 N. = Force of kinetic friction.
Fap*cos20-Fk = m*a
Fap*0.94-88.2 = 18*0 = 0
0.94Fap = 88.2
Fap = 93.9 N. = Force applied
b. Tension = Fap = 93.9 N.
c. Work=Fap*cos20o*d=93.9cos20 * 20=1764 J.
d. E = Fk*d = 88.2 * 20 = 1764 J.
Thanks!
To determine the force applied by the person to keep the crate moving at a constant speed, we need to consider the forces acting on the crate.
1. The weight of the crate: The weight of the crate can be calculated by multiplying the mass of the crate (18.0 kg) by the acceleration due to gravity (9.8 m/s^2).
Weight = mass * gravity
Weight = 18.0 kg * 9.8 m/s^2
Weight = 176.4 N
2. The normal force: The normal force is equal in magnitude and opposite in direction to the weight of the crate, acting perpendicular to the horizontal surface. In this case, the normal force will be equal to the weight of the crate.
Normal force = Weight
Normal force = 176.4 N
3. The force of kinetic friction: The force of kinetic friction is given by the equation:
Force of kinetic friction = coefficient of kinetic friction * normal force
Given that the coefficient of kinetic friction between the floor and the crate is 0.50, we can calculate the force of kinetic friction as follows:
Force of kinetic friction = 0.50 * Normal force
Force of kinetic friction = 0.50 * 176.4 N
Force of kinetic friction = 88.2 N
4. The force applied by the person: Since the crate is being pulled at a constant speed, the force applied by the person must cancel out the force of kinetic friction.
Force applied by the person = Force of kinetic friction
Force applied by the person = 88.2 N
So, the person must apply a force of 88.2 Newtons to keep the crate moving at a constant speed.