A 1250 kg car sits on an ice-covered ramp that rises 25.0° above the horizontal. The ramp is frictionless, and the car is held in place by a cable that makes a 31.0° angle with
the surface of the ramp as shown.
To solve this problem, we need to determine the tension in the cable that is holding the car in place on the ramp.
Let's break down the problem into its various components.
1. Draw a free body diagram: Start by drawing a free body diagram for the car. This will help us identify the forces acting on the car. In this case, we have the weight of the car (mg) acting vertically downward, the normal force (N) acting perpendicular to the ramp, and the tension in the cable (T) acting along the cable.
2. Resolve forces: Resolve the weight of the car into its components. Since the ramp is inclined at an angle of 25.0° above the horizontal, we can resolve the weight into two components: one parallel to the ramp (mg*sinθ) and one perpendicular to the ramp (mg*cosθ), where θ is the angle of inclination.
3. Apply Newton's second law: Apply Newton's second law (ΣF = ma) in the horizontal and vertical directions separately. In the vertical direction, the sum of forces should be equal to zero since the car is not accelerating vertically. Therefore, we have: N - mg*cosθ = 0.
4. Find the normal force: From the above equation, we can solve for the normal force (N): N = mg*cosθ.
5. In the horizontal direction, the only force acting is the component of the weight parallel to the ramp (mg*sinθ). This force is balanced by the tension in the cable, so we have: T = mg*sinθ.
Substituting the value of the weight (mg) and the angle of inclination (25.0°), we can find the tension in the cable.