Answer :
Final answer:
The work done by gravity on a 1200 kg roller coaster car moving 145 ft at a 40.0° angle below the horizontal to point B is approximately 418,749.12 joules, calculated by finding the vertical component of the displacement and multiplying it by the weight of the car.
Explanation:
To calculate the work done by gravity on a roller coaster car as it travels from point A to point B, with a displacement of 145 ft at a 40.0° angle below the horizontal, we need to consider the vertical component of the displacement. The force of gravity acting on the car is equal to the car's weight, which is the mass of the car (1200 kg) multiplied by the acceleration due to gravity (9.8 m/s2). This force will act in the vertical direction only.
The vertical displacement can be found by multiplying the total displacement by the sine of the angle of descent. Converting feet to meters (1 foot = 0.3048 meters), we have 145 ft * 0.3048 m/ft = 44.20 meters. The vertical displacement is then 44.20 meters * sin(40.0°).
Work done by gravity is the product of the force due to gravity and the vertical displacement in the direction of the force. So the work done by gravity is:
- Weight of the car (Fg) = mass (m) * acceleration due to gravity (g) = 1200 kg * 9.8 m/s2
- Vertical displacement (dy) = 44.20 m * sin(40.0°)
- Work (W) = Fg * dy = 1200 kg * 9.8 m/s2 * (44.20 m * sin(40.0°))
Work (W) = 1200 kg * 9.8 m/s2 * (44.20 m * 0.6428) ≈ 418,749.12 joules
Therefore, the work done by gravity on the roller coaster car during this displacement is approximately 418,749.12 joules.
