To find the magnitude of the force the car applies to the truck, we can use Newton's second law: force = mass × acceleration. First, we need to find the acceleration of the car and the truck together.
The net force acting on both the car and the truck is given by the difference between the force applied by the car (4500 N) and the rolling friction of the truck (765 N):
net_force = 4500 N - 765 N = 3735 N
The total mass of the car and the truck together is:
total_mass = 1200 kg + 2100 kg = 3300 kg
Using Newton's second law, we can find the acceleration of the car and the truck together:
acceleration = net_force / total_mass = 3735 N / 3300 kg ≈ 1.1318 m/s²
Now, we can find the force the car applies to the truck by considering only the truck. We know that the truck has a rolling friction of 765 N and that the car and the truck have the same acceleration. The net force acting on the truck must be equal to the product of the truck's mass and the acceleration:
net_force_truck = truck_mass × acceleration = 2100 kg × 1.1318 m/s² ≈ 2376.78 N
The force the car applies to the truck must be greater than the rolling friction to accelerate the truck. Therefore, the force that the car applies to the truck should be:
force_car_to_truck = net_force_truck + rolling_friction = 2376.78 N + 765 N ≈ 3141.78 N
The magnitude of the force the car applies to the truck is approximately 3141.78 N.
A 1200 -kg car is pushing an out-of-gear 2100 -kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push horizontally against the ground with a force of 4500 N . The rolling friction of the car can be neglected, but the heavier truck has a rolling friction of 765 N , including the "friction" of turning the truck's drivetrain. What is the magnitude of the force the car applies to the truck?
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