A boy weighing 40kg runs at 8.0m/s grabs a rope and swings of level ground. What maximum height does the child reach?
How do I solve this?? it is under the conservation of energy section of work, power and energy.
any help would be great! thanks
Assume his KE is transformed to gravitational potential energy.
how do i find gravitational potential energy without being given the height?
To determine the maximum height reached by the boy, we can use the conservation of mechanical energy principle.
The conservation of mechanical energy states that the total mechanical energy of a system, consisting of kinetic energy (KE) and potential energy (PE), remains constant when no external forces are acting on the system. Mathematically, it can be written as:
KE_initial + PE_initial = KE_final + PE_final
In this case, we can assume initial potential energy (PE_initial) is zero, as the boy starts from level ground. Also, we can assume final kinetic energy (KE_final) is zero, as the boy comes to rest at the maximum height.
Initially, the kinetic energy (KE_initial) is given by:
KE_initial = (1/2) * mass * velocity^2
Substituting the given values, we have:
KE_initial = (1/2) * 40 kg * (8.0 m/s)^2
= 1280 J
At the maximum height, all the kinetic energy is converted into potential energy (PE_final). The potential energy formula is given by:
PE_final = mass * gravitational acceleration * height
Rearranging the formula, we get:
height = PE_final / (mass * gravitational acceleration)
The mass of the boy is 40 kg and the gravitational acceleration (g) is approximately 9.8 m/s^2. Substituting these values and the initial kinetic energy into the height formula, we can calculate the maximum height reached by the boy.