A girl 36 kg occupies a seat of a swing that this subject by two chains 20 m in length each. If someone drops the girl from an 8 m position below the highest of the swing. What strength exercises it on the girl when she passes through the point lower?
she drops 20 - 8 = 12 meters
her los of potential energy in the drop is m g h = 12 m g Joules
her Ke is then 12 m g Joules
(1/2) m v^2 = 12 m g
so v^2 = 24 g
force up on girl -force down on girl = m a
F - m g = m v^2/r
F = m (g + v^2/r)
F = m (g + 24 g/20)
F = m g (1+24/20)
F = m g (2.2) = 36*9.8*2.2
To calculate the force exerted on the girl when she passes through the lowest point of the swing, we need to consider the gravitational force acting on her.
First, let's find the potential energy at the highest point of the swing. The potential energy (PE) is given by the formula:
PE = m * g * h
Where:
m = mass of the girl (36 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height (position) above the lowest point (8 m)
PE = 36 kg * 9.8 m/s^2 * 8 m
PE = 2822.4 J
Next, let's find the total mechanical energy at the lowest point of the swing. The total mechanical energy (E) is the sum of potential energy (PE) and kinetic energy (KE). At the lowest point, all of the potential energy is converted into kinetic energy, so the formula is:
E = PE + KE
Since the girl is at the lowest point, the height (h) is 0, so the potential energy (PE) is also 0. Thus, the total mechanical energy (E) is equal to the kinetic energy (KE).
E = KE
E = 2822.4 J
Now, let's find the velocity (v) at the lowest point using the kinetic energy formula:
KE = 1/2 * m * v^2
2822.4 J = 1/2 * 36 kg * v^2
v^2 = 2822.4 J * 2 / 36 kg
v^2 = 156.8 m^2/s^2
v ≈ √156.8 m^2/s^2
v ≈ 12.5 m/s
Now, let's calculate the magnitude of the force exerted on the girl at the lowest point using the centripetal force formula:
F = m * a_c
Where:
F = force
m = mass of the girl (36 kg)
a_c = centripetal acceleration
The centripetal acceleration can be calculated using the formula:
a_c = v^2 / r
Where:
v = velocity (12.5 m/s)
r = length of one chain (20 m)
a_c = (12.5 m/s)^2 / 20 m
a_c = 7.81 m/s^2
Now, we can calculate the force:
F = 36 kg * 7.81 m/s^2
F ≈ 281 N
Therefore, the force exerted on the girl when she passes through the lowest point of the swing is approximately 281 Newtons.