A 4900kg cable car goes 350m up a hill inclined 14∘ above the horizontal. What can your learn about the work done by the cable to move car up the hill? Answer quantitatively. Ignore friction.
1.5x10^7
To determine the work done by the cable car to move up the hill, we need to calculate the gravitational potential energy change of the car.
The work done (W) is given by the equation:
W = ΔPE = mgh
Where:
- W is the work done (in Joules)
- ΔPE is the change in gravitational potential energy (in Joules)
- m is the mass of the cable car (in kilograms)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height change (in meters)
In this case, the cable car goes up the hill with a certain height change. The height change can be calculated using the inclined height and the vertical height of the hill.
The vertical height (h) of the hill can be determined using the inclined height (d) and the angle of inclination (θ) using trigonometry:
h = d * sin(θ)
Substituting the given values:
- Inclined height (d) = 350 m
- Angle of inclination (θ) = 14 degrees
We can now calculate the vertical height (h) as follows:
h = 350 * sin(14)
Next, we substitute the values into the formula for work done:
W = mgh
W = 4900 * 9.8 * h
Finally, we substitute the value of h, calculate W, and get the work done by the cable car:
W = 4900 * 9.8 * (350 * sin(14))
Calculating this expression will give you the quantitative value of the work done by the cable car.