The driver of a 1600 kg car, initially traveling at 10.6 m/s, applies the brakes, bringing the car to rest in a distance of 23.0 m.
(a) Find the net work done on the car.
(b) Find the magnitude and direction of the force that does this work. (Assume this force is constant.)
a) net work equals the change in KE.
or, Vf^2=Vi^2+2ad solve for a
then work= force*distance= mass*a*distance.
b) force= ma
I worked out the first equation for part a and found the acceleration to be -0.2304. When doing the second equation, I found work to be -8478.72 J. Can work be negative? I feel like I haven't worked this out correctly.
I feel like the acceleration isn't correct.
To find the net work done on the car, we need to use the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy.
(a) To start, we need to calculate the initial kinetic energy of the car. The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
Here, the mass of the car is 1600 kg, and the initial velocity is 10.6 m/s. Substituting these values, we get:
Initial Kinetic Energy = (1/2) * 1600 kg * (10.6 m/s)^2
Next, we need to find the final kinetic energy, which is zero since the car comes to rest.
Final Kinetic Energy = 0
The net work done on the car is equal to the change in kinetic energy, given by the equation:
Net Work = Final Kinetic Energy - Initial Kinetic Energy
Substituting the values, we have:
Net Work = 0 - [(1/2) * 1600 kg * (10.6 m/s)^2]
Now, we can calculate the net work done on the car.
(b) To find the magnitude and direction of the force that does this work, we can use the work-energy principle again. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied:
Work = Force * Distance
Since the car comes to rest, the work done on it is equal to the net work calculated in part (a). Thus:
Net Work = Force * Distance
Substituting the values, we have:
0 - [(1/2) * 1600 kg * (10.6 m/s)^2] = Force * 23.0 m
Now, we can solve for the force that does this work. Dividing both sides of the equation by 23.0 m, we have:
Force = [0 - [(1/2) * 1600 kg * (10.6 m/s)^2]] / 23.0 m
Now, you can simplify this expression and calculate the magnitude and direction of the force.