1-A car is lifted a certain distance in a service station and therefore has potential energy with respect to the floor. If it were lifted twice as high, how much potential energy would it have?
Answer: twice as much
2-Two cars, one twice as heavy as the other, are lifted to the same elevation in a service station. How do there potential energies compare?
Answer: The heavy object has more potential energy?
Yes, the heavier car has twice as much potential energy as the lighter car.
Correct. The potential energy of an object is directly proportional to its height and mass. In the given scenario, when the two cars are lifted to the same elevation, the heavier car will have more potential energy compared to the lighter car.
To understand why the potential energy of an object increases when it is lifted higher, we need to know about the concept of potential energy.
1) The potential energy of an object is determined by its position relative to a reference point, usually the Earth's surface. When an object is lifted, it gains potential energy because work is done against gravity to move the object against its weight. The potential energy is given by the formula: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point.
So, if a car is lifted a certain distance, its potential energy with respect to the floor is proportional to its mass and the height it's lifted. Now, if the car is lifted twice as high, the value of 'h' in the formula becomes twice as large. Therefore, doubling the height will result in twice the potential energy. Hence, if the car is lifted twice as high, it will have twice as much potential energy.
2) Now, considering two cars, one twice as heavy as the other, both lifted to the same elevation in a service station. The potential energy of an object depends on its mass, height, and the acceleration due to gravity (g). Since both cars are lifted to the same height, the only variable affecting their potential energy is their mass.
As discussed earlier, potential energy (PE) is proportional to mass (m) and height (h). Thus, the heavier car will have more potential energy since it has a greater mass. Consequently, in this scenario, the heavy object has more potential energy compared to the lighter one.
In summary, the potential energy of an object is directly proportional to its mass and height. Increasing the height will result in an increase in potential energy, while increasing the mass will also increase the potential energy when the height is the same.