There is a van that is being pushed by a car. The car is pushing the van from the van's behind. The van's mass is 4M and the car's mass is M. If the max force that the ground can provide to the car's tires is F, then what are the max forces between the car and the van? . Consider that there are no other horizontal forces acting on the van
It depends on the motion of the two vehicles. We assume that both vehicles are on a horizontal surface.
If both are stationary, the maximum force is μs(4M)g, the frictional force of the car reisisting motion, at the point just before motion starts.
μs is the coefficient of static friction.
If they are both in uniform velocity, then the maximum force is then μk(4M)g
where μk is the coefficient of kinetic friction.
If both are accelerating at a rate of a m/s², then the maximum force is μk(4M)g+(4M)a.
All forces are in the direction of motion of the vehicles.
To find the maximum forces between the car and the van, we need to consider the forces acting on both objects and apply Newton's second law of motion.
Let's consider the forces on the van first. Since there are no other horizontal forces acting on the van, the only force acting on it is the force exerted by the car. According to Newton's third law of motion, the force exerted by the car on the van is equal in magnitude but opposite in direction to the force exerted by the van on the car.
Now, let's define the variables:
M = mass of the car
4M = mass of the van
F = maximum force the ground can provide to the car's tires
According to Newton's second law, the force on an object is equal to its mass multiplied by its acceleration. In this case, the van is being pushed by the car, so the acceleration of the van is the same as the acceleration of the car.
Therefore, the force on the van can be written as:
Force on the van = mass of the van × acceleration
And the force on the car can be written as:
Force on the car = mass of the car × acceleration
Since the force on the van and the car have the same magnitude but opposite directions, we can write:
Force on the van = (-1) × Force on the car
Since the acceleration is the same for both objects, we can cancel it out.
Now, we can express the forces in terms of the variable F:
Force on the van = (-1) × force on the car
4M × acceleration = (-1) × M × acceleration
Now, we can solve for the forces:
Force on the van = 4M × acceleration = 4M × F/M = 4F
Force on the car = (-1) × force on the van = (-1) × 4F = -4F
Therefore, the maximum force between the car and the van is 4F in the direction from the van towards the car.