Question

The 2.5-Mg four-wheel-drive SUV tows the 1.5-Mg trailer. The traction force developed at the wheels is FD = 5 kN

Part A- Determine the speed of the truck in 20 s , starting from rest.
Part B- Determine the tension developed in the coupling between the SUV and the trailer. Neglect the mass of the wheels.

Answer 1

To find the speed of the truck in 20 seconds, use the speed equation and the acceleration from Newton's second law. To find the tension in the coupling, calculate the net force acting on the trailer.

To determine the speed of the truck in 20 seconds, we can use the equation: speed = initial velocity + acceleration * time. Since the truck starts from rest, the initial velocity is 0. The acceleration can be found using Newton's second law: acceleration = net force / mass. So the acceleration is FD / total mass. Substituting the given values, we get: acceleration = 5 kN / (2.5 Mg + 1.5 Mg). Finally, we can use the speed equation to find the speed.

To determine the tension in the coupling between the SUV and the trailer, we need to find the net force acting on the trailer. The net force is equal to the applied force minus the force of friction. The force of friction can be found using the equation: force of friction = coefficient of friction * normal force. Assuming the trailer is on a level surface, the normal force is equal to the weight of the trailer. Substituting the given values, we can calculate the tension in the coupling.

Answer 2

Part A- The speed of the truck after 20 seconds is 0.04 m/s. Part B- The tension in the coupling between the SUV and the trailer is 5 kN.

Step-by-step explanation:

Part A- To determine the speed of the truck in 20 seconds, we can use the equation:

Speed = Initial Speed + (Acceleration x Time)

The initial speed is 0 since the truck starts from rest. The acceleration can be calculated using Newton's second law:

Force = Mass x Acceleration

Since the traction force developed at the wheels is 5 kN, we can convert it to Newtons (1 kN = 1000 N):

Force = 5 kN x 1000 N/kN = 5000 N

The mass of the truck is 2.5 Mg (1 Mg = 1000 kg), so:

5000 N = 2.5 Mg x Acceleration

Solving for acceleration:

Acceleration = 5000 N / (2.5 Mg) = 5000 N / (2.5 x 10^6 kg) = 0.002 m/s^2

Now we can plug this acceleration into the speed equation:

Speed = 0 + (0.002 m/s^2 x 20 s) = 0.04 m/s

Therefore, the speed of the truck after 20 seconds is 0.04 m/s.

Part B- To determine the tension developed in the coupling between the SUV and the trailer, we can use Newton's third law:

Force (SUV on trailer) = Force (trailer on SUV)

Since the traction force developed at the wheels is 5 kN, the force exerted by the SUV on the trailer is 5 kN. Therefore, the tension in the coupling between the SUV and the trailer is 5 kN.