Answer:
= 15.57 N
= 2.60 N
= 16.98 N
The mass of the bag is the same on the three planets. m=1.59 kg
Explanation:
The weight of the sugar bag on Earth is:
g=9.81 m/s²
m=3.50 lb=1.59 kg
=m·g=1.59 kg×9.81 m/s²= 15.57 N
The weight of the sugar bag on the Moon is:
g=9.81 m/s²÷6= 1.635 m/s²
=m·g=1.59 kg× 1.635 m/s²= 2.60 N
The weight of the sugar bag on the Uranus is:
g=9.81 m/s²×1.09=10.69 m/s²
=m·g=1.59 kg×10.69 m/s²= 16.98 N
The mass of the bag is the same on the three planets. m=1.59 kg
Answer:
A) = 1.44 kg m², B) moment of inertia must increase
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is
I = ½ m R²
A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is
I = + m D²
Let's apply these equations to our case
The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms
=
+ 2
= ½ M R²
The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body
M = 7/8 m total
M = 7/8 64
M = 56 kg
The mass of the arms is
m’= 1/8 m total
m’= 1/8 64
m’= 8 kg
As it has two arms the mass of each arm is half
m = ½ m ’
m = 4 kg
The arms are very thin, we will approximate them as a particle
= M D²
Let's write the equation
= ½ M R² + 2 (m D²)
Let's calculate
= ½ 56 0.20² + 2 4 0.20²
= 1.12 + 0.32
= 1.44 kg m²
b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase