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 determine the amount of force required to accelerate the car, we first need to understand the forces acting on the car. A free body diagram can help us visualize these forces.
Free body diagram:
```
|-----> F_applied
|
|-----> F_friction = 350 N (opposite direction of motion)
|
|-----> F_net
|
|-----> F_gravity
|
```
- F_applied: Force applied to the car to accelerate it.
- F_friction: Force of friction between the tires and the road, which opposes the motion of the car.
- F_net: Net force acting on the car, which is equal to the difference between the applied force and the friction force.
- F_gravity: Force due to gravity acting on the car, which is proportional to the car's mass.
From Newton's second law of motion, we know that the net force acting on an object is equal to the product of the object's mass and its acceleration:
F_net = m * a
In this case, the mass of the car is given as 1,000 kg, and we want to accelerate it to 15 m/s^2. Plugging in these values, we can rearrange the equation to solve for the net force:
F_net = (1,000 kg) * (15 m/s^2)
F_net = 15,000 N
Now, we know that the net force is equal to the difference between the applied force and the friction force:
F_net = F_applied - F_friction
Substituting the known values, we can solve for the applied force:
15,000 N = F_applied - 350 N
F_applied = 15,000 N + 350 N
F_applied = 15,350 N
Therefore, a force of 15,350 Newtons would be required to accelerate the 1,000-kg car to 15 m/s^2, given a frictional force of 350 N.