How much force would be required to accelerate a 1,000-kg car to 15 m/s 2 if the force of friction between the tires and the road was 350 N? Show your work and use appropriate units of measurement. Explain using a free body diagram.
To find the force required to accelerate the car, we need to analyze the forces acting on it. Let's start by drawing a free-body diagram for the car:
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Friction Applied Force
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The two forces acting on the car are the force of friction and the applied force. The force of friction always acts in the opposite direction to the motion and can be calculated using the equation:
Friction = coefficient of friction * Normal force
where the normal force is the force exerted by the ground on the car, which is equal to the weight of the car (mass * gravity).
Given that the force of friction is 350 N, we can rearrange the equation to solve for the normal force:
Normal force = Friction / coefficient of friction
Since the coefficient of friction is not given, we'll assume it is 1 (a rough estimate). Let's calculate the weight of the car:
Weight = mass * gravity
Using a standard gravity of 9.8 m/s^2:
Weight = 1000 kg * 9.8 m/s^2 = 9800 N
Now we can calculate the normal force:
Normal force = Friction / coefficient of friction = 350 N / 1 = 350 N
The applied force is the force required to accelerate the car. The equation for force is:
Force = mass * acceleration
Given that the mass of the car is 1000 kg and the acceleration is 15 m/s^2:
Force = 1000 kg * 15 m/s^2 = 15000 N
Therefore, the force required to accelerate the 1000 kg car to 15 m/s^2 is 15000 N.