A 1200 kg car accelerates to the right at 7m/s2 along a special frictionless track. Determine the magnitude and direction of the force the engine exerts to accelerate the car?
A wind blows heavy winds into the car's path.As a result the car's acceleration slows to 4.5m/s2. If the engine is exerting the same force it was in part a, how much force does the wind exert on the car to slow acceleration.
Part 1:
Use F = m a to solve for the engine force F, in Newtons
Part 2:
In this case F, the net force, is F = F(engine) - F(wind)
Use F(engine) from Part 1 and the new lower value of acceleration (a) to solve for F(wind)
F(air) = F(engine) - m a
Just as an aside: A car (at least, a car as we understand it, with four wheels rotating on the ground) would not be able to accelerate on a frictionless track. The force providing the acceleration is the frictional force between the tires and the track. Some sort of "air car" (using, for example, a big fan) would, however, be able to accelerate on a frictionless track.
To determine the magnitude and direction of the force the engine exerts to accelerate the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the mass of the car is given as 1200 kg, and the acceleration is 7 m/s^2 to the right.
Using the formula F = m * a, we can calculate the force exerted by the engine:
F = 1200 kg * 7 m/s^2
F = 8400 N
Therefore, the magnitude of the force the engine exerts to accelerate the car is 8400 N, and since the car is accelerating to the right, the direction of the force is also to the right.
Now, let's move on to part b, where the wind slows down the car's acceleration to 4.5 m/s^2. If the engine is still exerting the same force as in part a, we need to determine the force exerted by the wind.
Again, using Newton's second law, we can calculate the force exerted by the wind:
F = m * a
F = 1200 kg * (7 m/s^2 - 4.5 m/s^2)
F = 1200 kg * 2.5 m/s^2
F = 3000 N
Therefore, the force exerted by the wind to slow down the car's acceleration is 3000 N. The direction of this force would be opposite to the direction of the car's motion, so it would be to the left.