A 1070 kg hybrid car pushes a 2140 kg Jeep that has died on railroad tracks. If the wheels of the hybrid car push against the ground with 5890 N of force, what is the magnitude of the force between the hybrid car and the Jeep? Assume there is no rolling friction.
To find the magnitude of the force between the hybrid car and the Jeep, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
In this case, the force exerted by the hybrid car on the Jeep is equal in magnitude but opposite in direction to the force exerted by the Jeep on the hybrid car. So, to find the magnitude of the force between them, we need to determine the force exerted by the Jeep on the hybrid car.
Since there is no rolling friction, the only external forces acting on the hybrid car and the Jeep are the normal force and the force of friction. The normal force is equal to the weight of the bodies in this case, so we can calculate it as follows:
For the hybrid car:
Weight of the hybrid car = mass × acceleration due to gravity
= 1070 kg × 9.8 m/s²
≈ 10486 N
For the Jeep:
Weight of the Jeep = mass × acceleration due to gravity
= 2140 kg × 9.8 m/s²
≈ 20972 N
Since the normal force cancels out the weight of the bodies, the net external force is only due to the force of friction, which is also the force exerted by the Jeep on the hybrid car.
Now, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration is zero, as the Jeep is at rest.
Force of friction = mass × acceleration
= (1070 kg + 2140 kg) × 0 m/s²
= 0 N
Therefore, the magnitude of the force between the hybrid car and the Jeep is zero N, indicating that there is no force between them.
F = m a
5890 = (1070+2140) a
a = 5890/(1070+2140)
then
Fjeep = 2140 a