A 9-volt battery supplies 0.125 A of electrical current to a toy car. The car has a mass of 0.100 kg and the coefficient of friction between the tires and the ground is 0.4. If the car is 100% efficient, how far will the car travel in 10 seconds?
To determine how far the car will travel, we need to consider the forces acting on it. The only force that will move the car forward is the force of friction between the tires and the ground.
We can calculate the force of friction using the equation:
Force of friction = coefficient of friction * normal force
The normal force is the force exerted by the ground in the upward direction to balance the weight of the car. Since the car is on a flat surface, the normal force is equal to the weight of the car.
Weight of the car = mass * gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s² on Earth.
Once we have determined the force of friction, we can calculate the acceleration of the car using Newton's second law:
Force = mass * acceleration
Finally, we can use the kinematic equation to find the distance traveled by the car:
Distance = initial velocity * time + 0.5 * acceleration * time²
Since the car starts from rest, the initial velocity is 0.
Let's plug in the values and calculate the distance traveled:
Mass of the car (m) = 0.100 kg
Coefficient of friction (μ) = 0.4
Gravitational acceleration (g) = 9.8 m/s²
Time (t) = 10 s
Weight of the car = m * g = 0.100 kg * 9.8 m/s² = 0.98 N
Force of friction = μ * weight = 0.4 * 0.98 N = 0.392 N
Acceleration of the car = Force / mass = 0.392 N / 0.100 kg = 3.92 m/s²
Distance = 0 * 10 s + 0.5 * 3.92 m/s² * (10 s)² = 0 + 0.5 * 3.92 m/s² * 100 s² = 0 + 196 m = 196 m
Therefore, the car will travel a distance of 196 meters in 10 seconds.