A car has a maximum acceleration of 4.6m/s2 . What will the maximum acceleration be if the car is towing another car of the same mass?
To find the maximum acceleration when the car is towing another car of the same mass, we can consider the concept of Newton's second law of motion. According to this law, the force acting on an object is equal to its mass multiplied by its acceleration:
Force = Mass × Acceleration
In this case, the mass of the car and the towed car are the same. Let's denote the mass of the car as "m".
When the car is not towing another car, the maximum acceleration is given as 4.6 m/s^2. This means that the force exerted on the car to achieve this acceleration is:
Force1 = m × (4.6 m/s^2)
When the car is towing another car of the same mass, the total mass that needs to be moved is now twice the mass of the individual cars, i.e., 2m. To find the new maximum acceleration, we need to calculate the force required to achieve that acceleration:
Force2 = (2m) × Acceleration2
Since the force required to accelerate the cars is the same in both cases, we can equate the forces:
Force1 = Force2
m × (4.6 m/s^2) = (2m) × Acceleration2
Simplifying the equation, we find:
4.6 m/s^2 = 2 × Acceleration2
Now, we can solve for Acceleration2:
Acceleration2 = 4.6 m/s^2 / 2
Therefore, the maximum acceleration when the car is towing another car of the same mass will be half of the original maximum acceleration, which is 2.3 m/s^2.