The driver of a 1024 kg truck traveling 32.6 m/s North on I-77 has to make a sudden stop. If it requires a distance of 57.1 m for the truck to stop, use conservation of energy to find the net force acting on the truck.
Force x distance = work done against friction = initial kinetic energy
Solve for the force
F = (1/2) M Vo^2/X
To find the net force acting on the truck, we can use the principle of conservation of energy. According to this principle, the work done on the truck to bring it to a stop is equal to the change in its kinetic energy.
The work done on the truck can be calculated using the formula:
Work = Force * Distance
Let's denote the net force acting on the truck as F_net. The work done by this force is given by:
Work = F_net * 57.1 m
The initial kinetic energy of the truck is given by:
K_initial = (1/2) * mass * velocity^2
Substituting the given values, we have:
K_initial = (1/2) * (1024 kg) * (32.6 m/s)^2
The final kinetic energy of the truck, when it comes to a stop, is zero. Therefore, the change in kinetic energy is:
ΔK = 0 - K_initial
Since work is equal to the change in kinetic energy, we have:
F_net * 57.1 m = -K_initial
Solving for the net force (F_net), we get:
F_net = (-K_initial) / 57.1 m
Now, let's calculate the net force acting on the truck:
F_net = [(-1/2) * (1024 kg) * (32.6 m/s)^2] / 57.1 m
Evaluating the expression, we find:
F_net = - 94474.5955 N
Therefore, the net force acting on the truck is approximately -94474.6 N.
Note: The negative sign indicates that the force is acting in the opposite direction to the motion (i.e., opposite to the north direction).