How do I find the recoil velocity of the earth immediately after the popper popped?
Using the conservation of momentum law.
Please someone help me. This is due in 30mins
To find the recoil velocity of the Earth immediately after the popper popped, we need to consider the principles of conservation of momentum.
The conservation of momentum states that the total momentum of an isolated system remains constant before and after an event (in the absence of external forces). The momentum of an object is given by the product of its mass and velocity.
In this case, the Earth and the popper constitute an isolated system. Initially, before the popper was popped, the Earth and the popper were at rest, so their total momentum was zero.
When the popper is popped, it ejects compressed gas in one direction. According to Newton's third law of motion, for every action there is an equal and opposite reaction. Therefore, the ejected gas will exert an equal and opposite force on the Earth.
To find the recoil velocity of the Earth, you will need to know the mass of the popper, the mass of the Earth, and the velocity at which the gas is expelled from the popper. Once you have this information, you can use the conservation of momentum to calculate the recoil velocity of the Earth.
The momentum before the popper is popped is zero, so the momentum after the popper is popped must also be zero to obey the conservation of momentum. The momentum of the gas expelled in one direction will be equal in magnitude but opposite in direction to the momentum of the Earth.
Using the equation for momentum: momentum = mass × velocity
We can set up the equation:
(mass of Earth) × (recoil velocity of Earth) = (mass of gas expelled) × (velocity of gas expelled)
Rearranging the equation, you can solve for the recoil velocity of the Earth:
(recoil velocity of Earth) = [(mass of gas expelled) × (velocity of gas expelled)] / (mass of Earth)
By plugging in the respective values, you can find the recoil velocity of the Earth immediately after the popper popped.