Question

A car with a mass of 1500 kg is being towed by a rope held at an angle to the horizontal. A friction force of 320 N opposes the car's motion. What is the tension in the rope if the car goes from rest to 12 m/s in 10 s?

Answer 1

To find the tension in the rope, calculate the net force acting on the car by considering the gravitational force and the friction force. Use the given values to find the tension in the rope.

Step-by-step explanation:

To find the tension in the rope, we need to consider the forces acting on the car. The gravitational force acting on the car can be calculated using the equation: force = mass x acceleration due to gravity. The friction force opposing the car's motion is given as 320 N. The net force acting on the car can be calculated using the equation: force = mass x acceleration. Since the car goes from rest to 12 m/s in 10 s, we can calculate the acceleration using the equation: acceleration = change in velocity / time. Substitute the given values to find the net force. The tension in the rope is equal to the net force acting on the car minus the friction force. Substitute the values to find the tension in the rope.

Let's calculate:

1. Gravitational force: force = 1500 kg x 9.8 m/s² = 14700 N
2. Acceleration: acceleration = (12 m/s - 0 m/s) / 10 s = 1.2 m/s²
3. Net force: force = 1500 kg x 1.2 m/s² = 1800 N
4. Tension in the rope: tension = 1800 N - 320 N = 1480 N

Therefore, the tension in the rope is 1480 N.