Biomedical measurements show that the arms and hands together typically make up 13.0% of a person's mass, while the legs and feet together account for 37.0% . For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. Let us consider a 78.0kg person having arms 69.0cm long and legs 94.0 cm long. The person is running at 12.0km/h, with his arms and legs each swinging through +-30 in 1/2s . Assume that the arms and legs are kept straight.
a)What is the average angular velocity of his arms and legs?
i got 2.09 its correct
b) Using the average angular velocity from part A, calculate the amount of rotational kinetic energy in this person's arms and legs as he walks.
Krot=? J
i solved this first ML= .37*78= 28.86kg
MA= .13*78= 10.14 kg
what do i do next im confused
C)What is the total kinetic energy due to both his forward motion and his rotation?
Ktotatl=? J
Part D) What percentage of his kinetic energy is due to the rotation of his legs and arms?
i know i have to Krot/ktotal to solve my problem
b) To calculate the amount of rotational kinetic energy in this person's arms and legs as he walks, you need to use the formula for rotational kinetic energy:
Krot = (1/2)Iω^2,
where Krot is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.
Since the arms and legs are modeled as thin uniform bars, the moment of inertia can be calculated using the formula:
I = (1/3)mL^2,
where m is the mass and L is the length of the bar.
For the arms:
m = 10.14 kg (as you correctly calculated)
L = 69.0 cm = 0.69 m
For the legs:
m = 28.86 kg (as you correctly calculated)
L = 94.0 cm = 0.94 m
Now you can calculate the moment of inertia for the arms and the legs, respectively:
Iarms = (1/3)(10.14 kg)(0.69 m)^2
Ilegs = (1/3)(28.86 kg)(0.94 m)^2
Once you have the moment of inertia, you can calculate the rotational kinetic energy for the arms and the legs, respectively:
Krot_arms = (1/2)(Iarms)(ω)^2
Krot_legs = (1/2)(Ilegs)(ω)^2
c) To calculate the total kinetic energy due to both forward motion and rotation, you need to consider both translational kinetic energy and rotational kinetic energy.
First, calculate the translational kinetic energy:
Ktrans = (1/2)mv^2,
where m is the mass of the person (78.0 kg) and v is the velocity of the person (12.0 km/h = 3.33 m/s).
Then, calculate the total kinetic energy:
Ktotal = Ktrans + Krot_arms + Krot_legs.
d) To calculate the percentage of the total kinetic energy that is due to the rotation of the legs and arms, you can use the formula:
Percentage of rotational kinetic energy = (Krot_arms + Krot_legs)/Ktotal * 100.