A car of mass 800kg is climbing an incline at 10° to the horizontal. Determine the increase in potential energy of the car as it moves a distance of 50m up the incline.
Question
A car of mass 800kg is climbing an incline at 10° to the horizontal. Determine the increase in potential energy of the car as it moves a distance of 50m up the incline.
Solution
To solve this problem, we need to use the formula for gravitational potential energy, which is PE = mgh, where:
- PE is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity
- h is the height
However, since the car is moving up an incline, we need to find the vertical height (h) the car has climbed. We can do this using trigonometry, as the car is moving along the hypotenuse of a right triangle. The sine of the angle (10°) is equal to the opposite side (height) divided by the hypotenuse (50m). So, h = 50m * sin(10°).
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First, calculate the height (h): h = 50m * sin(10°) = 8.71m (approx)
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Then, substitute m = 800kg, g = 9.8m/s² (approx), and h = 8.71m into the formula: PE = mgh = 800kg * 9.8m/s² * 8.71m = 68,264.8 Joules (approx)
So, the increase in potential energy of the car as it moves a distance of 50m up the incline is approximately 68,264.8 Joules.
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