A spaceship lands on the planet whose radius is 5 times that of planet earth and whose mass is 25 times that of planet earth. Find the apparent weight of the astronaut on the second planet if the astronaut weighs 150lbs on planet earth
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radius 5x, makes Gravity 1/25th
mass= 25x, makes the graviaty 25x
so it looks like the person weights 150lbs on that planet.
To find the apparent weight of the astronaut on the second planet, we need to understand the relationship between weight, mass, and gravity.
The weight of an object is given by the formula:
Weight = mass × gravity
Where gravity is the acceleration due to gravity on the specific planet.
Now, let's start by determining the gravity on the second planet. The intensity of the gravitational field on a planet is given by the formula:
gravity = (G × mass) / (radius^2)
Where G is the gravitational constant, approximately equal to 6.67 × 10^(-11) N m^2/kg^2.
For the second planet, with a radius 5 times that of Earth and a mass 25 times that of Earth, we can plug in these values to calculate the gravity on the second planet.
radius of the second planet = 5 × radius of Earth
mass of the second planet = 25 × mass of Earth
Plugging these values into the formula for gravity, we get:
gravity = (G × mass of the second planet) / (radius of the second planet^2)
Now, let's calculate the gravity on the second planet:
gravity = (6.67 × 10^(-11) N m^2/kg^2 × 25 × mass of Earth) / (5 × radius of Earth)^2
Next, we can calculate the weight of the astronaut on the second planet using the formula:
Weight = mass × gravity
Since we know the weight of the astronaut on Earth is 150lbs, we need to convert it to mass in kilograms. 1 pound is approximately equal to 0.454 kilograms.
Weight on the second planet = mass × gravity
Weight on the second planet = (150lbs × 0.454 kg/lb) × gravity
Now we can substitute the calculated value of gravity into the equation to find the apparent weight of the astronaut on the second planet.