Two cars travel at the same speed, so that they move 105 km in one hour. One car, a sleek
sports car, has a motor that delivers only 35 kW of power at this speed. The other car
needs its motor to produce 65 kW to move the car this fast. The difference is caused by air
resistance.
a. For each car, list the external horizontal forces exerted on it, and give the cause of each
force. Compare their magnitudes.
b. By Newton’s third law, the car exerts forces on the ground and the air. What are their directions?
c. Calculate the magnitude of the forward frictional force exerted by each car.
d. The car engines did work. Where did the energy come from?
a. The external horizontal forces exerted on each car are:
1) Frictional force from the ground which propels the car forward, caused by the contact between the tires and the ground.
2) Air resistance (drag force), which acts in the opposite direction of the car's motion, caused by the interaction between the car and air molecules.
The magnitudes of the frictional force and air resistance for each car are different due to their different power requirements (35 kW for the sports car and 65 kW for the other car).
b. By Newton's third law, the car exerts an equal and opposite force on the ground and the air. The directions of these forces are:
1) The force exerted on the ground by the car is in the opposite direction of the frictional force (backward).
2) The force exerted on the air by the car is in the opposite direction of the air resistance (forward).
c. To calculate the magnitude of the forward frictional force exerted by each car, we will use the following equation:
Power = Force × Velocity
For the sports car:
35,000 W (35 kW) = Force × (105,000 m / 3,600 s)
Force = 35,000 × 3,600 / 105,000
Force ≈ 1,200 N
For the other car:
65,000 W (65 kW) = Force × (105,000 m / 3,600 s)
Force = 65,000 × 3,600 / 105,000
Force ≈ 2,240 N
Hence, the forward frictional force exerted by the sports car is about 1,200 N and by the other car is about 2,240 N.
d. The energy required for the car engines to do work came from the fuel (for example, gasoline) that the engines burned. The chemical energy stored in the fuel was converted into mechanical work to propel the cars forward.
a. For the sleek sports car:
- External horizontal force: Air resistance
- Cause of force: Air molecules colliding with the car's surface, creating resistance
- Magnitude: Not given in the information provided
For the car needing 65 kW:
- External horizontal force: Air resistance
- Cause of force: Air molecules colliding with the car's surface, creating resistance
- Magnitude: Not given in the information provided
b. By Newton’s third law, the car exerts forces on the ground and the air. The forces are in opposite directions to the external forces mentioned in part a.
c. To calculate the magnitude of the forward frictional force exerted by each car, we need additional information about the coefficient of friction or other relevant factors. The information provided does not allow us to calculate it.
d. The energy for the car engines comes from the fuel or power source used by each car. The sleek sports car requires 35 kW, and the other car needs 65 kW, indicating different power requirements and, potentially, different types of fuel or power sources used.
a. For each car, the external horizontal forces exerted on it can be listed as follows:
1. Sleek sports car:
- Driving force: This force is exerted by the motor of the car, propelling it forward. In this case, the driving force is caused by the motor delivering 35 kW of power.
- Air resistance force: This force opposes the motion of the car due to the resistance offered by the air. In this case, it causes a decrease in the car's speed and requires the motor to exert additional power to maintain a constant speed.
2. Other car:
- Driving force: Similar to the sleek sports car, this force is exerted by the motor of the car, enabling it to move forward. However, the motor in this car needs to produce 65 kW of power to maintain the same speed as the sleek sports car.
- Air resistance force: As in the case of the sleek sports car, this force opposes the motion and demands additional power from the motor to counteract the air resistance.
Comparing their magnitudes, we can see that the driving force required in the other car is greater (65 kW) compared to the sleek sports car (35 kW) to achieve the same speed. This difference in power requirement is due to the increased air resistance faced by the other car.
b. By Newton's third law, the cars exert equal and opposite forces on the ground and the air. The direction of these forces can be understood as follows:
1. Sleek sports car:
- Force on the ground: The sleek sports car exerts a downward force on the ground due to its weight, as per Newton's third law. This force is equal and opposite to the force the ground exerts on the car, keeping it in equilibrium.
- Force on the air: The sleek sports car pushes the air backward as it moves forward, creating an equal and opposite force on the air.
2. Other car:
- Force on the ground: Similar to the sleek sports car, the other car also exerts a downward force on the ground due to its weight, following Newton's third law. This force is balanced by the equal and opposite force exerted by the ground.
- Force on the air: The other car also pushes the air backward while moving forward, generating an equal and opposite force on the air.
c. To calculate the magnitude of the forward frictional force exerted by each car, we need more information regarding their masses, contact area with the ground, and the coefficient of friction between their tires and the road surface. Without this information, it is not possible to determine the exact value of the forward frictional force.
d. The energy required to move the cars comes from the fuel they consume. The engines in both cars convert the chemical energy stored in the fuel into mechanical energy to power the vehicles. As the engines burn the fuel, they release energy that is harnessed to generate the driving force, enabling the cars to move.