imagine a bouncing ball that does not lose any energy as it bounces. could it ever bounce to a greater height than it was droppe
d from? explain your answer
2 answers:
Answer:
No, due to conservation of energy, the bouncing ball would need to create energy in order to bounce higher.
Explanation:
The question says that the ball was dropped, so we suppose that it will start at an initial velocity of zero. (If the ball was tossed, then it's initial velocity would be greater than zero and it would bounce accordingly, but it would never bounce higher than it's maximum height)
Due to conservation of energy, the energy of the ball will remain the same throughout its trip. As the ball travels down to the ground, its potential energy decreases while its kinetic energy will increase, its sum will remain constant. When the ball hits the ground, it will have its maximum kinetic energy, which is equal to its potential energy (the energy the ball started with). The energy is transmited to the ground and back to the ball (supposing the bounce is completely elastic and no energy was lost as heat or vibration).
So the ball starts its way back up. The height it can reach will depend on its potential energy, since energy remains constant (energy is not created nor destroyed), the ball can only get as high as it was originaly dropped from sine its mass and the acceleration of gravity remains constant.
Take a look at the uploaded diagram which represents the given situation.
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Answer:
Part a: When the road is level, the minimum stopping sight distance is 563.36 ft.
Part b: When the road has a maximum grade of 4%, the minimum stopping sight distance is 528.19 ft.
Explanation:
Part a
When Road is Level
The stopping sight distance is given as
Here
- SSD is the stopping sight distance which is to be calculated.
- u is the speed which is given as 60 mi/hr
- t is the perception-reaction time given as 2.5 sec.
- a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
- G is the grade of the road, which is this case is 0 as the road is level
Substituting values
So the minimum stopping sight distance is 563.36 ft.
Part b
When Road has a maximum grade of 4%
The stopping sight distance is given as
Here
- SSD is the stopping sight distance which is to be calculated.
- u is the speed which is given as 60 mi/hr
- t is the perception-reaction time given as 2.5 sec.
- a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
- G is the grade of the road, which is given as 4% now this can be either downgrade or upgrade
For upgrade of 4%, Substituting values
<em>So the minimum stopping sight distance for a road with 4% upgrade is 528.19 ft.</em>
For downgrade of 4%, Substituting values
<em>So the minimum stopping sight distance for a road with 4% downgrade is 607.59 ft.</em>
As the minimum distance is required for the 4% grade road, so the solution is 528.19 ft.