To find the initial height at which the child starts, we use the equation 2.3 * (1 - cos(25)).
h_initial = 2.3 * (1 - cos(25))
h_initial ≈ 0.47 m
The potential energy (PE) at the initial position is given by:
PE_initial = m * g * h_initial
PE_initial = 49 kg * 9.8 m/s^2 * 0.47 m
PE_initial ≈ 227.2 J
At the lowest position, the child has kinetic energy (KE) given by:
KE_final = 0.5 * m * v^2
KE_final = 0.5 * 49 kg * (1.83818 m/s)^2
KE_final ≈ 83.0 J
The mechanical energy dissipated by various resistive forces is the difference between the initial potential energy and the final kinetic energy:
Energy_dissipated = PE_initial - KE_final
Energy_dissipated = 227.2 J - 83.0 J
Energy_dissipated ≈ 144.2 J
Thus, the mechanical energy dissipated by various resistive forces is approximately 144.2 J.
Draw the figure, and calcuate the height above the bottom point the swing starts. (I remember it as 2.3(1-cos25)).
the initial energy is mg*height.
The final energy is 1/2 m v^2
The difference is frction.
A 49 kg child on a 2.3 m long swing is released
from rest when the swing supports make an
angle of 25 degrees with the vertical.
The acceleration of gravity is 9.8 m=s2 :
If the speed of the child at the lowest po-
sition is 1.83818 m=s, what is the mechani-
cal energy dissipated by the various resistive
forces (e.g. friction, etc.)? Answer in units of
J.
1 answer
1 answer