A 1200 kg car on a horizontal surface starts from rest and accelerates uniformly to 72 km/h in 20.0 s. Friction exets an average force of 450 N on the car during this time.
a) what is the net work done on the car
b) how far does the car move during this acceleration
now i knoq W=fxd but how else could i get it!!!! and how does the friction work in?
I know I'm 10 years late to this problem, but there's more steps to the problem that are missing, and friction doesn't come into play until those problems. Change km/h to m/s to get 20m/s, then KE=(1/2)mv^2 is the formula. The answer comes out to 2.4e5 J.
To find the net work done on the car, you can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy. Since the car starts from rest, the initial kinetic energy is 0. The final kinetic energy can be calculated using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the car (m) = 1200 kg
Final velocity (v) = 72 km/h = 20 m/s (converted from km/h to m/s)
Final kinetic energy = (1/2) * m * v^2
Now, you have the final kinetic energy and the initial kinetic energy is 0. Therefore, the net work done on the car is equal to the change in kinetic energy, which is:
Net Work = Final Kinetic Energy - Initial Kinetic Energy = Final Kinetic Energy - 0 = Final Kinetic Energy
To calculate the final kinetic energy, substitute the given values into the formula:
Final Kinetic Energy = (1/2) * 1200 kg * (20 m/s)^2
Now, calculate the final kinetic energy to find the net work done on the car.
To calculate the distance the car moved during this acceleration, you can use the equation for displacement of an object under uniform acceleration:
Displacement (d) = (1/2) * acceleration * time^2
Given:
Acceleration = ?
Time (t) = 20.0 s
The average force of friction (F) exerted on the car during this time is given as 450 N. The net force acting on the car is the sum of the applied force (required to accelerate the car) and the force of friction. Therefore, net force (F_net) is:
F_net = F_applied + F_friction
Since the car is accelerating uniformly, the net force is equal to the mass of the car (m) multiplied by the acceleration (a):
F_net = m * a
Now, you can solve for acceleration:
a = F_net / m
Substitute the given values to find the acceleration:
a = (450 N) / (1200 kg)
Now that you have the acceleration, substitute it and the given time (t) into the displacement formula to find the distance the car moved during this acceleration.
To find the net work done on the car, you can use the work-energy principle. The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy.
a) To calculate the net work done on the car, you need to find the initial and final kinetic energies of the car. First, convert the final velocity from km/h to m/s.
Final velocity = 72 km/h = (72 * 1000) / 3600 = 20 m/s.
The initial velocity is 0 m/s since the car starts from rest. Therefore, the change in kinetic energy is:
ΔKE = 0.5 * m * (vf^2 - vi^2),
where m is the mass of the car and vf and vi are the final and initial velocities, respectively.
Plugging in the values:
ΔKE = 0.5 * (1200 kg) * (20 m/s)^2 - 0.5 * (1200 kg) * (0 m/s)^2,
= 0.5 * (1200 kg) * (20 m/s)^2,
= 240,000 J.
So, the net work done on the car is 240,000 J.
b) To find the distance the car moves during this acceleration, you can use the equation for average acceleration:
a = (vf - vi) / t,
where vf is the final velocity, vi is the initial velocity, and t is the time.
Plugging in the values:
20 m/s = (vf - 0 m/s) / (20.0 s),
vf = (20 m/s) * (20.0 s),
vf = 400 m.
So, the car moves a distance of 400 meters during this acceleration.
Now, let's address the role of friction. The question states that friction exerts an average force of 450 N on the car during this time. Friction always acts in the direction opposite to the motion, so it opposes the car's motion and acts to slow it down. Since the car is accelerating, the force of friction opposes the forward motion and is responsible for decelerating the car.
The work done by friction can be found using the equation:
W = f * d * cos(θ),
where f is the force, d is the distance, and θ is the angle between the force and the displacement. In this case, θ is 180 degrees since friction acts opposite to the displacement.
Plugging in the values:
W = (450 N) * (400 m) * cos(180 degrees),
W = (450 N) * (400 m) * (-1),
W = -180,000 J.
The negative sign indicates that the work done by friction is in the opposite direction of the displacement, consistent with the fact that friction is acting to oppose the car's motion.