how does height affects speed?

Question

im doing a science coursework on how the height of a ramp affects the speed at which a marble rolls down it I need some information on how height affects speed. If anyone can help tht would be great thanks!

I know the higher the ramp the faster the marble will go down but i need to know why with explanations using kenetic energy etc

Answer 1

The gravitational potential energy of the marble is equal to mgh, where m is the mass, g is the acceleration due to gravity, and h is the height from which the marble starts. Assuming no friction, this energy will all be converted to kinetic energy by the bottom of the ramp. Kinetic energy equals 1/2m times v squared (half mass times velocity squared).

Due to the complete conversion of grav. pot. energy to kinetic, you can equate the two above equations, therefore

mgh = 1/2mv^2

divide by m (remember do the same to both sides)

gh = 1/2 v^2

multiply by 2

2gh = v^2

square root of both sides, and turn the equation round:

v = Square root (2gh)

And there's your answer - the velocity equals the square root of 2 times g times the height.

Think I deserve more than two points for doing your homework for you ;o)

Would I make a good physics teacher?

Answer 2

To a point, the higher the ramp, the faster the marble will roll, same as the higher you drop it, the faster it falls, to a point. That point is the point at which the marble reaches termnal velocity, i.e. it is going as fast as it possibly can here on Earth, and a higher drop or longer ramp won't make any difference. The difference between the ramp and the drop is caused by coefficient of kinetic friction, and the angle at which the marble is falling/rolling with respect to the plane of the surface of the Earth.

Answer 3

While increasing the height does increase the potential energy, giving further 'down' to roll, the speed (which is measured in meters per second) is affected by the amount of time it has to be accelarated by gravity. Remember that gravity is pulling down not just in meters-per-second but in meters-per-second-per-second. This means that every second it is allowed to act on the marble it is moving it even faster than in the last second. The longer distance you are giving it with the taller ramp is actually just giving gravity more time to speed it up even faster. Hope this helps

Answer 4

mass x gravity x height gives you the potential energy that the marble will change into kinetic.

The kinetic energy will be 1/2 x mass x (velocity squared)

from that you can work out the velocity.

Actually it will be a bit slower than that because of friction, and the energy consumed in making that rumbling noise that marbles make on ramps, not to mention the thunk when it reaches the bottom

Answer 5

increasing he height of the ramp means also increasing thevalue of potential energy. the higher the potential energy the more kinetic energy will be used as the marble rolls down the ramp, therefore the marble will go faster.

tried to explain in a way which helped me when i was stuying the same topic. hope i help.

Answer 6

Hieght effects speed because the hieght of the ramp causes the marble to go faster because the hiegher the the rampo the more air or ramp time the marble will get and gain speed

Answer 7

Height affects the potential energy of the marble. By using conservation of energy, we can assume that the marble has the same energy at the top of the ramp as as the bottom.

(top) E = E (bottom)

The energy at each location is composed of two different types, potential and kinetic. Potential energy is the product of mass, gravity, and height. Kinetic is equal to half of the product of mass and the square of velocity.

mgh + 0.5*m*v^2 = mgh + 0.5*m*v^2

Because the marble is not moving at the top of the ramp, velocity at that point is zero. Also, when the marble reaches the bottom, the height at the end is zero. Using this, we can find the velocity of the object based on the height it started at.

mgh + 0.5*m*0^2 = mg*0 + 0.5*m*v^2

mgh = 0.5*m*v^2

v = (2*g*h)^(0.5)

If you must account for rotational kinetic energy (since the marble is rolling), you must add in 0.5 * I * w^2, where I is the moment of inertia for the rotating object and w is the rotational velocity. So, if we were to use the original equation, it would look like this:

mgh + 0.5*m*v^2 + 0.5*I*w^2 = mgh + 0.5*m*v^2 + 0.5*I*w^2

Just as before, we assume that the object is not moving at the top of the ramp (v=0,w=0) and that it has reached the bottom at the end of the ramp (h=0).

mgh + 0.5*m*0^2 + + 0.5*I*0^2 = mg*0 + 0.5*m*v^2 + 0.5*I*w^2

mgh = 0.5*m*v^2 + 0.5*I*w^2

Then we can substitute in for the moment of inertia and the rotational velocity. The moment of inertia for a sphere is 0.4*mass*radius^2. Rotational is equal to (v^2)/(r^2).

mgh = 0.5*m*v^2 + 0.5 * 0.4*m*r^2 * (v^2)/(r^2)

The r^2 cancels, leaving

mgh = 0.5*m*v^2 + 0.5 * 0.4*m*v^2

Divide through by mass.

gh = 0.5*v^2 + 0.5 * 0.4*v^2

gh = (0.5 + 0.2)*v^2

v = (10/7 * gh)^(0.5)

Answer 8

The higher the ramp te greater the GRADIENT. Which means the velocity of the marble will increase so greater kenetic energy.

Answer 9

I wasn't useful no remember in case you meant an prolonged ramp of a ramp it particularly is top is replaced because of the fact of a much better inclination so stuff approximately inclination is first, length is 2d. properly the forces appearing on it are the downward tension of gravity, friction (till you're assuming gentle floor?) and the conventional reaction, everyday reaction is the slope pushing back against the automobile. it rather is the tension of gravity that makes the automobile go down it, its length is R= mg sin(theta) the place R is the tension, m= mass, g= gravity (9.8) and theta= the attitude of inclination of the slope. forget approximately approximately this paragraph if the ramp its travelling down is gentle. appearing by contrast tension is friction this is given by potential of F=(mu)N the place mu= coefficient of friction and N is the conventional reaction and is given by potential of mg cos(theta). m, g and theta are all the comparable as for the downward tension of gravity. in case you enhance the attitude theta then R gets greater by way of sin (sin gets greater between 0-ninety tiers). additionally F gets smaller because of the fact the conventional reaction gets smaller as theta will enhance (cos gets smaller between 0-ninety tiers). All this final paragraph potential is that the bigger the attitude of inclination the bigger the consequent tension, a greater resultant tension will enhance the acceleration (from Newton's 2d regulation - F=ma) and hence speed. hence the consequent tension= R-F. Combining those with F=ma: R-F= ma. All that covers the acceleration and forces appearing on it. Now speed= u + at, the place u = preliminary speed, a= acceleration and t= time. Presuming your automobile starts at relax its speed is merely it rather is acceleration x time. So the longer your automobile travels the swifter it gets, hence in case you have an prolonged ramp it could holiday swifter. Lol sorry with regards to the size of the reason, while you're no longer clean on any of it merely ask :)

Answer 10

starts as potential. its called grafity for 1 then you have momentum 2 then you got the stoping factor of a solid force. next time just google or yahoo search for momentum or how phycis work ok.