A 42-kg girl is bouncing on a trampoline. During a certain interval after leaving the surface of the trampoline, her kinetic energy decreases to 220 J from 460 J. How high does she rise during this interval? Neglect air resistance.
Just wondering how to solve this.
The kinetic energy decrease (240 J) equals her potential energy increase: (M*g*deltaY)
Delta Y is her increase in elevation during that time, which is
240J/(M*g) = 0.583 m
To solve this problem, we can use the conservation of energy principle, which states that the total energy of a system remains constant if no external forces, such as air resistance, are acting on it. In this case, we need to consider the gravitational potential energy and the kinetic energy of the girl.
Let's break down the problem step by step:
1. Calculate the initial kinetic energy (KEi) of the girl using the formula:
KEi = 460 J
2. Calculate the final kinetic energy (KEf) of the girl using the formula:
KEf = 220 J
3. Since the total energy is conserved, we can equate the initial kinetic energy to the sum of the final kinetic energy and the change in gravitational potential energy (ΔPEg).
KEi = KEf + ΔPEg
4. To calculate the change in gravitational potential energy, we can use the formula:
ΔPEg = m * g * h
Where:
m is the mass of the girl = 42 kg
g is the acceleration due to gravity = 9.8 m/s^2
h is the height above the starting point
5. Rearrange the equation to solve for h:
ΔPEg = m * g * h
ΔPEg - KEf = m * g * h
h = (ΔPEg - KEf) / (m * g)
Now let's substitute the values into the equation:
ΔPEg = (KEi - KEf) = (460 J - 220 J) = 240 J
m = 42 kg
g = 9.8 m/s^2
h = (240 J - 220 J) / (42 kg * 9.8 m/s^2)
h = 20 J / (411.6 kg * m^2/s^2)
h ≈ 0.0485 m
Therefore, the girl rises approximately 0.0485 meters during this interval.