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. Consider surface friction, and air friction.
b. the car tire tries to push the earth back, and the earth resists equal and opposite.
d. Duh, chemical?
a. For the sleek sports car, the external horizontal forces exerted on it are:
1. Thrust force from the motor: This force is caused by the power generated by the motor and propels the car forward.
2. Air resistance force: This force is caused by the interaction of the car with the surrounding air and opposes the motion of the car.
For the other car, the external horizontal forces exerted on it are:
1. Thrust force from the motor: This force is caused by the power generated by the motor and propels the car forward.
2. Air resistance force: This force is also present, as air resistance affects both cars equally.
Comparing their magnitudes:
Since both cars are traveling at the same speed and covering the same distance in one hour, we can infer that the magnitudes of the external horizontal forces on both cars are equal.
b. According to Newton's third law, for each action, there is an equal and opposite reaction. Therefore, both cars exert forces on the ground and the air in the opposite direction to their motion.
For both cars, the force exerted on the ground is in the backward direction (opposite to the motion of the cars). The force exerted on the air is also in the backward direction.
c. To calculate the magnitude of the forward frictional force exerted by each car, we need some additional information. The question does not provide the coefficient of friction or any specific details about the surfaces involved. The frictional force depends on the coefficient of friction between the tires and the road.
d. The car engines convert chemical energy stored in fuel into mechanical energy to perform work. In this case, the energy comes from the gasoline or fuel source used by the cars. The engines combust the fuel, converting it into kinetic energy that powers the cars and overcomes the external forces like air resistance and friction.
a. For the sleek sports car, the external horizontal forces exerted on it are:
1. Air resistance: This force is caused by the air particles pushing against the car as it moves forward. The magnitude of this force is related to the shape and aerodynamics of the car, as well as the air density and speed. The exact magnitude can be difficult to determine without more information.
2. Frictional force: This force is exerted by the tires of the car on the road surface to propel the car forward. The magnitude of this force depends on factors such as the weight of the car, the type of tires, and the condition of the road.
For the other car that needs 65 kW of power, the external horizontal forces exerted on it are:
1. Air resistance: Similar to the sleek sports car, this force is caused by the air particles pushing against the car as it moves forward. The magnitude of this force may be higher due to the car's less aerodynamic shape in comparison to the sports car.
2. Frictional force: Just like the sports car, this force is exerted by the tires of the car on the road surface to propel the car forward. The magnitude of this force also depends on factors such as the weight of the car, the type of tires, and the condition of the road.
b. According to Newton's third law, for both cars, the forces exerted by the cars on the ground and the air are equal in magnitude and opposite in direction to the forces exerted by the ground and air on the cars. The force exerted by the car on the ground is directed downwards, while the force exerted by the car on the air is directed rearward.
c. To calculate the magnitude of the forward frictional force exerted by each car, more information is needed. Factors such as the weight of the car, the type of tires, and the condition of the road are needed to determine the precise value of the frictional force. The magnitude of the frictional force can be calculated using the formula F = µN, where F is the frictional force, µ is the coefficient of friction, and N is the normal force.
d. The energy that powers the car engines comes from the fuel used by the cars. When the fuel is burned, it releases chemical energy, which is then converted into mechanical energy to propel the cars forward.