Show with proof, the planet which an astronaut would have a greater weight if Planet A has twice the mass and twice the radius o
1 answer:
Answer:
First let's look at the gravitational formula by newton:
Now the f and g should be capital but that's not possible with the equation system. But we can see that the force the astronaut is pulled at is dependent on the mass and the distance if we assume his mass stays the same (mass and weight aren't the same also g is a constant). If a planet has twice the radius the force will by four times as weak because of the ^2. This is not compensated by the twice as big mass. Therefore the astronaut will have a higher force and thus a higher weight on planet B
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while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
. So we can write
that we can solve to find an expression for v:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
that we can solve to find an expression for v: