An astronaut weighs 99 N on the Moon, where the acceleration of gravity is 1.62
m/s
2. How much does she weigh on Earth?
99N * 9.81/1.62 = _____ N
To find the weight of the astronaut on Earth, we need to know the acceleration due to gravity on Earth. The standard value of acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Given:
Weight on the Moon (W_moon) = 99 N
Acceleration due to gravity on the Moon (g_moon) = 1.62 m/s^2
Acceleration due to gravity on Earth (g_earth) = 9.8 m/s^2
We can use the formula relating weight, mass, and acceleration due to gravity:
Weight = mass * acceleration due to gravity
Let's calculate the mass of the astronaut first.
W_moon = mass * g_moon
Rearranging the formula, we get:
mass = W_moon / g_moon
Substituting the given values, we have:
mass = 99 N / 1.62 m/s^2
mass ≈ 61.11 kg
Now, let's calculate the weight of the astronaut on Earth.
W_earth = mass * g_earth
Substituting the known values:
W_earth = 61.11 kg * 9.8 m/s^2
W_earth ≈ 599.68 N
Therefore, the astronaut would weigh approximately 599.68 N on Earth.