2. A force of 2300 N [E] acts on a 900 kg car for 8 s. At the same time a friction force of 600 N [W] acts. What will the final speed of the car be? How far will it have travelled? How much work was done by the accelerating force? What is the kinetic energy of the car? How much energy was lost to friction? What was the rate of power loss to friction?
I have the answers however i have no idea how to derive them, or even where to start. Please help!
Thank You!
Net force=mass*acceleration
2300E-600E=900*a
solve for acceleration a.
vf=a*t
d=1/2 a t^2
Work=force*distance=2300*d
KEcar=1/2 m vf^2
Friction=600*d
rate power loss=friction work/8
To find the final speed of the car, you can use Newton's second law, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. The net force acting on the car is the difference between the applied force and the friction force:
Net force = Applied force - Friction force
Given:
Applied force = 2300 N [E]
Friction force = 600 N [W]
Mass of the car = 900 kg
Now, substitute these values into the equation and solve for the acceleration:
Acceleration = (Applied force - Friction force) / Mass
Acceleration = (2300 N [E] - 600 N [W]) / 900 kg
To subtract the forces, you need to consider their directions. Since the applied force is in the east direction and the friction force is in the west direction, you subtract their magnitudes:
Acceleration = (2300 N - 600 N) / 900 kg
Acceleration = 1700 N / 900 kg
Acceleration ≈ 1.89 m/s²
To find the final speed of the car, you can use the equation of motion:
Final velocity = Initial velocity + (Acceleration * Time)
Given:
Initial velocity = 0 m/s (assuming the car starts from rest)
Time = 8 s
Now, substitute the values into the equation and solve for the final velocity:
Final velocity = 0 m/s + (1.89 m/s² * 8 s)
Final velocity ≈ 15.12 m/s
To find the distance the car traveled, you can use the kinematic equation:
Distance = Initial velocity * Time + (0.5 * Acceleration * Time²)
Substitute the values and solve for the distance:
Distance = 0 m/s * 8 s + (0.5 * 1.89 m/s² * (8 s)²)
Distance ≈ 60.48 m
To calculate the work done by the accelerating force, you can use the equation:
Work = Force * Distance
Substitute the values and solve for the work:
Work = 2300 N * 60.48 m
Work ≈ 139.51 kJ (kilojoules)
To find the kinetic energy of the car, you can use the equation:
Kinetic energy = 0.5 * Mass * (Final velocity)²
Substitute the values and solve for the kinetic energy:
Kinetic energy = 0.5 * 900 kg * (15.12 m/s)²
Kinetic energy ≈ 102,419.2 J (joules)
To calculate the energy lost to friction, you can use the equation:
Energy lost = Friction force * Distance
Substitute the values and solve for the energy lost:
Energy lost = 600 N * 60.48 m
Energy lost ≈ 36.29 kJ (kilojoules)
Finally, to find the rate of power loss to friction, you can use the equation:
Power = Energy / Time
Substitute the values and solve for the power:
Power = 36.29 kJ / 8 s
Power ≈ 4.54 kW (kilowatts)
So, the final speed of the car is approximately 15.12 m/s, it traveled roughly 60.48 meters, the work done by the accelerating force is approximately 139.51 kJ, the kinetic energy of the car is about 102,419.2 J, the energy lost to friction is approximately 36.29 kJ, and the rate of power loss to friction is roughly 4.54 kW.