A space traveler weighs 635 N on earth. What will the traveler weigh on another planet whose radius is three times that of earth and whose mass is twice that of earth?
how did u answer it ?!
To find out what the traveler would weigh on another planet, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67 * 10^-11 N m^2 / kg^2)
m1 is the mass of the first object (the traveler)
m2 is the mass of the second object (the planet)
r is the distance between the centers of the two objects (the radius of the planet)
First, let's calculate the values we need:
Given:
Weight of the traveler on Earth (W) = 635 N
Mass of Earth (m2) = m
Radius of Earth (r) = R
We know that weight is calculated as the gravitational force acting on an object, so we can set up the equation as follows:
Weight of the traveler on Earth (W) = (G * m1 * m) / R^2
To find the weight of the traveler on the other planet, let's call the mass of the traveler m1'. We don't know this value yet, but we can solve for it.
Weight of the traveler on the other planet (W') = (G * m1' * 2m) / (3R)^2
Since we want to compare the weight on Earth to the weight on the other planet, we can set up the equation as a ratio:
(W') / (W) = [(G * m1' * 2m) / (3R)^2] / [(G * m1 * m) / R^2]
Now we can simplify the equation:
(W') / (W) = [(2m * m1') / (9R^2)] / (m1 / R^2)
Notice that we can cancel out the gravitational constant G since it appears in both the numerator and denominator.
(W') / (W) = (2m * m1' * R^2) / (9R^2 * m1)
Canceling out the R^2 and m1 terms:
(W') / (W) = (2m1') / (9m1)
Now we can solve for m1', the mass of the traveler on the other planet:
(W') = (2m1' * W) / (9)
To find the weight of the traveler on the other planet, we substitute the given weight on Earth (W = 635 N) into the equation:
(W') = (2m1' * 635 N) / (9)
At this point, we need the ratio of the radius of the other planet to the radius of Earth.
Given that the radius of the other planet (r') is three times that of Earth (3R), we can express the equation as:
(W') = (2m1' * 635 N) / (9) = (G * m1' * 2m) / (3R)^2
(W') = (635 N * 2m1') / 9 = (6.67 * 10^-11 N m^2 / kg^2) * (m1' * 2m) / (9 * (3R)^2)
Now we can substitute the given values:
(W') = (635 N * 2m1') / 9 = (6.67 * 10^-11 N m^2 / kg^2) * (m1' * 2m) / (9 * (3R)^2)
Let's evaluate the expression:
635 N * 2 / 9 = 1270 N / 9
Finally, substituting everything back into the equation:
(W') = (1270 N / 9) = (6.67 * 10^-11 N m^2 / kg^2) * (m1' * 2m) / (9 * (3R)^2)
Simplifying further, we get:
(W') ≈ (6.67 * 10^-11 N m^2 / kg^2) * (m1' * 2m) / ((9 * 9 * 9) * R^2)
(W') ≈ (6.67 * 10^-11 N m^2 / kg^2) * (m1' * 2m) / (729 * R^2)
(W') ≈ (m1' * 2m) / (729 * R^2) * (6.67 * 10^-11 N m^2 / kg^2)
Now we can substitute the values into the equation to calculate the weight on the other planet.