Calculating Speed from a Falling Ball's Gravitational Energy

In summary, the conversation discussed how to calculate the height a 1.00 Kg ball would have to fall freely to reach a speed of 100 Km/h. The equation used was \Delta E_g = \Delta E_k, which was then expanded to mgh' - mgh = \frac{1}{2}m(v')^2 - \frac{1}{2}mv^2. After simplifying and solving for h', the correct answer was obtained by plugging in the correct units, resulting in a height of 39.4 meters.
  • #1
Senjai
104
0

Homework Statement



How far would a 1.00 Kg ball have to fall freely to reach a speed of 100 Km/h ?

Homework Equations



[tex] \Delta E_g = \Delta E_k [/tex]

The Attempt at a Solution



[tex] \Delta E_g = \Delta E_k [/tex]

i then expanded to:

[tex] mgh' - mgh = \frac{1}{2}m(v')^2 - \frac{1}{2}mv^2 [/tex]

i got rid of the 1/2's and the mass

and 0'd out the equatiosthat would equal zero…

[tex] 2gh' = -(v')^2 [/tex]
[tex] h' = \frac{-(v')^2}{2g} [/tex]

subbed in the variables and ot 5.1 x 10^2 J.. which is wrong..

appreciate any help... thanks.
 
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  • #2
you got height in terms of Joules?
 
  • #3
the answer i got was 5.1 x 10^2 Joules, if that's what your asking...
 
  • #4
Joules is the unit of work, not height (the answer you have to calculate in #1 is height). Even if you talking about the energy content of the ball, its not 5.1 x 10^2 J.
 
  • #5
sorry i meant meters, I am actually not sure if its is meters... m/s / N/kg?

anyways, so let's go with meters. stil can't solve the answer..
 
  • #6
:confused: still I don't understand why you are not getting the answer. You have the equation with you, just plugin the values in your last equation and get the answer (I got 39.4 m)
 
Last edited:
  • #7
howd you get that? i still get 510...
 
  • #8
using

[tex] h' = \frac{-(v')^2}{2g}[/tex]
 
  • #9
Check your units... you plugged in v as 100 kph and g as 9.8 m/s[tex]^{2}[/tex]
 
  • #10
oh shii, unit conversion... sorry...
 

1. How do you calculate the speed of a falling ball using gravitational energy?

To calculate the speed of a falling ball using gravitational energy, you can use the equation: v = √(2gh), where v is the speed, g is the acceleration due to gravity, and h is the height of the ball.

2. What is the relationship between gravitational energy and speed of a falling ball?

The speed of a falling ball is directly proportional to its gravitational energy. This means that as the gravitational energy increases, the speed of the ball will also increase.

3. Can the speed of a falling ball be calculated without considering gravitational energy?

No, the speed of a falling ball cannot be accurately calculated without considering gravitational energy. This is because the force of gravity is what causes the ball to accelerate, thus affecting its speed.

4. How does the mass of the ball affect the speed calculation?

The mass of the ball does not directly affect the speed calculation, but it does affect the gravitational energy. The heavier the ball, the greater the gravitational energy, and therefore the higher the speed.

5. What other factors may affect the accuracy of the speed calculation from gravitational energy?

Other factors that may affect the accuracy of the speed calculation include air resistance, the shape and size of the ball, and the surface on which it is falling. These factors may alter the acceleration of the ball and thus affect its speed.

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