A 1200 kg car pulls a 510 kg trailer. The car exerts a horizontal force of 4040 N against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.160 for the trailer.
.160*4040=(1710)a
solve for a.
now, on the trailer,
f=510*a
To find the force that the car exerts on the trailer, we need to consider the forces acting on both the car and the trailer.
Let's first analyze the forces acting on the car. The only horizontal force acting on the car is the force exerted against the ground, which we'll call F_car. This force is given as 4040 N. Therefore, F_car = 4040 N.
Next, let's consider the forces acting on the trailer. There are three forces acting on the trailer:
1. The force exerted by the car: This is the force we want to find and denote as F_trailer.
2. The force of friction: The frictional force acts against the motion of the trailer and is given by the equation F_friction = μ * N, where μ is the friction coefficient and N is the normal force. In this case, the normal force is equal to the weight of the trailer, which is given by N = m_trailer * g. Here, m_trailer is the mass of the trailer (510 kg) and g is the acceleration due to gravity (9.8 m/s²). Therefore, N = 510 kg * 9.8 m/s² = 4998 N. Substituting the values, we have F_friction = 0.160 * 4998 N = 799.68 N.
3. The force of tension: This is the force in the tow cable connecting the car and the trailer, and it is equal to the force exerted by the car on the trailer (F_trailer).
Now, we can set up the equation of motion for the car and trailer system. According to Newton's second law, the net force applied to the system is equal to the product of the total mass and the acceleration:
Net force = (m_car + m_trailer) * acceleration.
In this case, the only acceleration we have is the acceleration of the car, as the trailer follows the same acceleration. The total mass is the sum of the car and trailer masses:
m_total = m_car + m_trailer = 1200 kg + 510 kg = 1710 kg.
Rearranging the equation, we can solve for the acceleration:
acceleration = Net force / m_total.
Substituting the given force and mass values, we have:
acceleration = 4040 N / 1710 kg = 2.364 m/s².
Now, we can calculate the force exerted by the car on the trailer (F_trailer) using the equation of motion for the trailer:
Net force_trailer = m_trailer * acceleration = F_trailer - F_friction.
Rearranging the equation and substituting the known values, we get:
F_trailer = Net force_trailer + F_friction = m_trailer * acceleration + F_friction.
Plugging in the values, we have:
F_trailer = 510 kg * 2.364 m/s² + 799.68 N = 1241.44 N + 799.68 N = 2041.12 N.
Therefore, the force that the car exerts on the trailer is approximately 2041.12 N.