How many times as high to achieve twice speed

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In summary, the conversation pertains to the conservation of energy and solving for the height of a ramp in order to achieve a certain velocity at the bottom. By setting up the equation mgh = 1/2*m*v^2, the group determines that the new ramp must be 4 times as high in order to achieve a speed of 2v instead of v.
  • #1
fattydq
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A block initially at rest is allowed to slide down a frictionless ramp and attains a speed of v at the bottom. In order to achieve a speed of 2v instead at the bottom, how many times as high must the new ramp be?

What laws does this pertain to? I don't really know where to start.
 
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  • #2
It pertains to the conservation of energy.
mgh = 1/2*m*v^2.
 
  • #3
rl.bhat said:
It pertains to the conservation of energy.
mgh = 1/2*m*v^2.

But I don't understand...velocity is only on one side of that equation. So how would you work it out for this problem?
 
  • #4
Exactly! What you have is the height of an object as a function of it's speed at the end. So if you know you must be a height, h, to achieve a velocity v, what must h be in order to achieve 2v?
 
  • #5
Pengwuino said:
Exactly! What you have is the height of an object as a function of it's speed at the end. So if you know you must be a height, h, to achieve a velocity v, what must h be in order to achieve 2v?

2h, but it says the answer is 4 times as high...that's what's confusing me...I don't know how to reach this final answer of 4.
 
  • #6
Nevermind, haha, I got it. Thanks a lot! Sorry for being a bit slow on the uptake : P
 

What does "twice speed" mean in this context?

"Twice speed" refers to an increase in velocity by a factor of two, or doubling the original speed.

What units are used to measure "high" in this scenario?

"High" can be measured in various units depending on the context, such as meters, feet, or kilometers.

Can "high" and "speed" be interchanged in this question?

No, "high" and "speed" have different meanings in this context. "High" refers to the height or altitude, while "speed" refers to the rate of motion.

Is the increase in height directly proportional to the increase in speed?

No, the increase in height needed to achieve twice the speed is not always directly proportional to the original height or speed. It depends on various factors such as air resistance, gravity, and the initial velocity.

What scientific principles can explain how to achieve twice the speed?

The principles of acceleration, momentum, and force can explain the relationship between height and speed. For example, increasing the height will increase the potential energy, which can be converted into kinetic energy to achieve twice the speed.

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