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You find yourself on your bike at the top of Twin Peaks in San Francisco. You are facing a 600m
descent. You and your bike weigh a combined 85 kg.
1. How much gravitational potential energy do you have before your descent? 600 m X 85 kg X 9.8 m/s/s = _______________________
2. You descend. If all that potential energy is converted to kinetic energy, what will your speed be at the bottom? Speed = ½ ms2
3. Name two other places to which your potential energy of gravity was transferred besides kinetic energy. _______________ and __________________. How will this manifest itself in your speed at the bottom of the hill? ___________________________ (No numerical answer is needed here.)
To find the answers to the questions, we need to apply the principles of gravitational potential energy and conservation of energy.
1. To calculate the gravitational potential energy before the descent, we can use the formula:
Gravitational Potential Energy = mass x gravity x height
Given that the height is 600m and the combined weight of you and your bike is 85kg, we can substitute these values into the formula:
Gravitational Potential Energy = 85kg x 9.8 m/s^2 x 600m
Calculating this equation will give us the answer to question 1.
2. To find the speed at the bottom of the descent, we can utilize the principle of conservation of energy. The potential energy at the top of the hill (Gravitational Potential Energy) will be converted into kinetic energy at the bottom of the hill. The equation for kinetic energy is:
Kinetic Energy = 0.5 x mass x speed^2
Setting Gravitational Potential Energy equal to Kinetic Energy, we can solve for speed:
Gravitational Potential Energy = Kinetic Energy
mass x gravity x height = 0.5 x mass x speed^2
Canceling out the mass from both sides of the equation:
gravity x height = 0.5 x speed^2
To find the speed, rearrange the equation:
speed = √(2 x gravity x height)
Substitute the given values for gravity (= 9.8 m/s^2) and height (= 600m) into the equation to calculate the speed at the bottom of the descent.
3. The potential energy of gravity is converted into other forms of energy during the descent. Two examples are:
- Heat energy: Some of the potential energy will be converted into heat due to air resistance and friction between the tires and the road.
- Sound energy: As the bike moves downhill, it might create sound vibrations.
These forms of energy will not affect the speed at the bottom of the hill directly. However, they indicate that not all the potential energy is converted into kinetic energy. Thus, the actual speed at the bottom of the hill might be slightly less than the calculated speed.