Step-by-step explanation:
To solve this problem, we can use the principle of conservation of mechanical energy. The total mechanical energy of the child-swing system will remain constant if we neglect friction.
a) To find the child's speed at the lowest position, we can use the conservation of mechanical energy. The total mechanical energy of the system consists of potential energy (due to the height) and kinetic energy:
Initial energy = Final energy
Initially, the child is at rest, so the initial kinetic energy is zero. The initial potential energy is given by the formula: PE_initial = m * g * h, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the initial vertical displacement.
At the lowest position, the potential energy becomes zero, and all the initial potential energy is converted into kinetic energy:
PE_initial = KE_final
m * g * h = (1/2) * m * v^2
Simplifying the equation:
h = (1/2) * v^2 / g
Plugging in the values:
h = (1/2) * (2.2 m/s)^2 / 9.8 m/s^2 ≈ 0.2505 m
Now, we can use trigonometry to find the vertical displacement:
sin(37°) = h / 2 m
h = 2 m * sin(37°) ≈ 1.213 m
Therefore, the child's speed at the lowest position is approximately 2.2 m/s.
b) To calculate the energy loss due to friction, we need to know the distance traveled by the child from the lowest position to the point where the speed is 2.2 m/s. However, this information is not provided in the question. Without knowing the distance or any other information related to friction, it is not possible to determine the energy loss due to friction.