A 2000 kg car pushes a 3000 kg truck that has a dead battery. The ground pushes forward on the car with a force of 6000 N. What is the magnitude of the force that the truck exerts on the car? Ignore any friction forces.
My work/attempts:
I've drawn a for body diagram for the two of them but am unsure how to solve for the Force sine I am not given an acceleration/velocity/etc.
well, I suppose they both have the same acceleration, call it a
The total mass is 5000 kg
The total force on the system is 6000 N
so
a = 6000/5000 = (6/5) m/s^2
Now how much of that is on the truck?
F = 3000 a = 3000 (6/5) = 3600 Newtons
from the car on the truck
so the force the truck exerts on the car is -3600 Newtons (third law, equal magnitude and opposite direction)
To solve this problem, let's use Newton's second law, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, we are given the mass of the car (2000 kg) pushing the truck (3000 kg) and the force exerted by the ground on the car (6000 N). We need to find the magnitude of the force that the truck exerts on the car (let's call it F_t).
First, let's find the acceleration of the car. Since the car is pushing the truck, and there is no friction or other forces acting on the car-truck system, the force exerted by the ground on the car (6000 N) is equal to the force exerted by the car on the truck:
F_ca = F_t
Using Newton's second law, we can write:
m_ca * a_ca = F_ca
Substituting the given values:
(2000 kg) * a_ca = 6000 N
Solving for a_ca:
a_ca = 6000 N / 2000 kg = 3 m/s^2
Now that we have the acceleration of the car, let's use it to find the magnitude of the force that the truck exerts on the car. Since the car and truck are in contact and exerting forces on each other, Newton's third law states that these forces are equal in magnitude and opposite in direction:
F_t = -F_ca
Substituting the values:
F_t = -(3000 kg) * (3 m/s^2) = -9000 N
Therefore, the magnitude of the force that the truck exerts on the car is 9000 N.