Answer
Since the truck is traveling on an incline, we need to consider both gravitational potential energy and kinetic energy. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work done on the truck is due to the force of friction, which is acting against the motion of the truck, and is given by:
W_friction = F_friction * d = (mgsin(theta)*mu)*d
where F_friction is the force of friction, d is the distance the truck skids before coming to rest, m is the mass of the truck, g is the acceleration due to gravity, theta is the angle of the incline, and mu is the coefficient of friction.
The change in kinetic energy of the truck is given by:
Delta K = (1/2)mv^2
where v is the initial velocity of the truck.
Since the truck comes to rest at the end of its skid, the final kinetic energy is zero. Therefore, the net work done on the truck is equal to its initial kinetic energy, and we have:
W_friction = Delta K
Substituting in the expressions for W_friction and Delta K, we get:
(mgsin(theta)*mu)*d = (1/2)mv^2
Simplifying and solving for d, we get:
d = (v^2)/(2gsin(theta)*mu)
Substituting in the given values, we get:
d = (20^2)/(29.81sin(10)*0.30) = 198.6 meters
Therefore, the truck will skid about 198.6 meters before coming to rest.
Work Step by Step
Since the truck is traveling on an incline, we need to consider both gravitational potential energy and kinetic energy. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work done on the truck is due to the force of friction, which is acting against the motion of the truck, and is given by:
W_friction = F_friction * d = (mgsin(theta)*mu)*d
where F_friction is the force of friction, d is the distance the truck skids before coming to rest, m is the mass of the truck, g is the acceleration due to gravity, theta is the angle of the incline, and mu is the coefficient of friction.
The change in kinetic energy of the truck is given by:
Delta K = (1/2)mv^2
where v is the initial velocity of the truck.
Since the truck comes to rest at the end of its skid, the final kinetic energy is zero. Therefore, the net work done on the truck is equal to its initial kinetic energy, and we have:
W_friction = Delta K
Substituting in the expressions for W_friction and Delta K, we get:
(mgsin(theta)*mu)*d = (1/2)mv^2
Simplifying and solving for d, we get:
d = (v^2)/(2gsin(theta)*mu)
Substituting in the given values, we get:
d = (20^2)/(29.81sin(10)*0.30) = 198.6 meters
Therefore, the truck will skid about 198.6 meters before coming to rest.
