a girl on a swing 2m above the ground at her highest point and 1m above the ground at her lowest point. what is the girls maximum speed?
Loss in P.E = Gain in K.E
mgh = 1/2mv^2
g(1) = 1/2v^2
2g = v^2
v = √19.6 = 4.427 m/s (Answered)
If I understand conservation of energy correctly, if her weight is mg, then the loss of PE going from 2m to 1m is mg Joules.
So, since that is converted to KE, we have
mg = 1/2 mv^2
2g = v^2
v = √19.6 m/s
?? whats the Answers....
To find the girl's maximum speed on a swing, we can use the principle of conservation of mechanical energy. When the girl is at her highest point, all her potential energy has been converted to kinetic energy. At this point, her potential energy is the highest and her kinetic energy is zero. When the girl is at her lowest point, all her kinetic energy has been converted to potential energy. At this point, her kinetic energy is the highest and her potential energy is zero.
The formula for potential energy is given by:
Potential Energy = m * g * h
Where:
m is the mass of the object (in this case, the girl)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height above a reference point (in this case, the ground)
The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * m * v^2
Where:
m is the mass of the object
v is the velocity of the object
Since the girl is at her highest point, all her potential energy is converted into kinetic energy. Therefore, we can equate the two equations:
m * g * h = (1/2) * m * v^2
We can simplify the equation by canceling out the mass (m) from both sides:
g * h = (1/2) * v^2
Now, we can solve for the maximum velocity (v) by rearranging the equation:
v = √(2 * g * h)
Substituting the values given in the question, we get:
v = √(2 * 9.8 * 2)
v ≈ √(39.2)
v ≈ 6.26 m/s
Therefore, the girl's maximum speed on the swing is approximately 6.26 m/s.