Answer :
Final answer:
The tension in the wire between the first car and the engine on an inclined plane can be found by using the gravitational force component down the incline. By calculating the mass times gravity times the sine of the incline angle, you can determine that the tension is approximately 101.2 kN.
Explanation:
To find the tension in the steel wire between the first car and the engine of a diesel engine weighing 50.0 ton that is at rest on the track inclined at an angle of 10.5°, we need to consider the forces acting along the incline. The total weight of the engine and the car is the sum of their weights, which is (50 ton + 2.2 ton) × 1000 kg/ton = 52.2 ton × 1000 kg/ton = 52200 kg. The force due to gravity acting down the incline can be calculated using the component of the weight along the incline, mg sin(θ), where m is the mass and θ is the incline angle.
The gravitational force is Fg = m × g × sin(θ), where g is the acceleration due to gravity (9.81 m/s²). Plugging in the values: Fg = 52200 kg × 9.81 m/s² × sin(10.5°) gives us the force in newtons, which can be converted to kilonewtons (kN) by dividing by 1000.
After calculating, you find the tension is approximately 101.2 kN, which is closest to option B.
