Earth of mass 6×10^24 kg is in motion around the sun with a linear velocity of magnitude 30 km/s.
a) Determine the magnitude of the linear momentum of the center of mass of Earth.
b) Is this linear momentum conseved?
Linear momentum: mv (change km to m)
Yes, it is conserved, as the sun is also rotating around the center of gravity of E-Sun system. The direction of the Sun's momentum at any point is equal and opposite to that of Earth.
To determine the magnitude of the linear momentum of the center of mass of Earth, we can use the formula:
Linear momentum (p) = mass (m) * velocity (v)
a) Given that the mass of Earth is 6 × 10^24 kg and the linear velocity is 30 km/s, we need to convert the velocity to m/s first:
30 km/s = 30,000 m/s
Now, we can calculate the linear momentum:
Linear momentum (p) = (6 × 10^24 kg) * (30,000 m/s)
p ≈ 1.8 × 10^29 kg·m/s
Therefore, the magnitude of the linear momentum of the center of mass of Earth is approximately 1.8 × 10^29 kg·m/s.
b) Yes, the linear momentum of the Earth's center of mass is conserved. According to the law of conservation of linear momentum, in the absence of any external forces acting on the Earth, the total linear momentum remains constant.
To determine the magnitude of the linear momentum of the center of mass of Earth, we need to use the equation:
Momentum = mass x velocity
a) The mass of the Earth is given as 6 x 10^24 kg, and the linear velocity is given as 30 km/s. However, we need to convert the velocity from km/s to m/s, since the standard SI unit for mass is kilograms.
Conversion:
30 km/s = 30,000 m/s (since 1 km = 1,000 m)
Now we can calculate the linear momentum of the center of mass:
Momentum = mass x velocity
= (6 x 10^24 kg) x (30,000 m/s)
To express this answer in scientific notation, we multiply the two values together and adjust the exponent accordingly:
= 180 x 10^24 kg*m/s
= 1.8 x 10^26 kg*m/s
Therefore, the magnitude of the linear momentum of the center of mass of Earth is 1.8 x 10^26 kg*m/s.
b) As for whether this linear momentum is conserved, we need to consider the forces acting on the Earth. In the absence of external forces, linear momentum is conserved, meaning the total momentum remains constant. However, in reality, there are other forces at play, such as gravity from the Sun and other celestial bodies, which can affect the linear momentum of the Earth. Therefore, in this context, the linear momentum is not strictly conserved.