### Physics Problem - Car Accelerating Up a Hill #### Problem Statement A 1650 kg car accelerates up a hill by applying a force of \( 4.61 \times 10^3 \) N parallel to the hill. The hill is at an incline of 13°.  Key details: - Mass of the car: \( 1650 \, \text{kg} \) - Applied force parallel to the hill: \( 4.61 \times 10^3 \, \text{N} \) - Incline angle of the hill: 13° - Initial velocity of the car (\( v_0 \)): \( 16 \, \text{m/s} \) - Distance traveled (\( d \)): \( 17 \, \text{m} \) #### Questions **a.** What is the net work done on the car as it travels 17 m up the hill? - *Hint*: Calculate the work done by each force in the system. There are three forces. The net work is the sum of the works done by each individual force. **b.** What is the change in kinetic energy for the car? **c.** The car is traveling at a speed of \( 16 \, \text{m/s} \) at the bottom of the hill. How fast is it moving at the top of the hill? #### Diagrams The diagram shows a car on an inclined plane. - The inclined plane is at an angle of 13°. - The car is moving a distance \( d = 17 \, \text{m} \) up the slope. - The initial velocity \( v_0 \) of the car is \( 16 \, \text{m/s} \). ### Explanation of Forces There are three primary forces acting on the car: 1. **Applied Force \( F_{\text{applied}} \)**: The force parallel to the hill, which is given as \( 4.61 \times 10^3 \, \text{N} \). 2. **Gravitational Force \( F_{\text{gravity}} \)**: The component of the car's weight acting parallel and perpendicular to the incline. 3. **Normal Force \( F_{\text{normal}} \)**: The perpendicular force exerted by