A man weighs 1220 N on Earth. What would he weigh on Jupiter, where the free-fall acceleration is 25.9 m/s2? The acceleration of gravity is 9.8 m/s2 .
Answer in units of N.
The weight on any planet is mg, where g is the appropriate acceleration due to gravity.
On earth, it is mg = 1220N, therefore
m = 1220/g
On Jupiter,
mg' = 1220/g*g'
= 1220*(25.9/9.8) N
= ? N
To find the weight of the man on Jupiter, we can use the formula:
Weight = Mass * Acceleration due to gravity
On Earth, the acceleration due to gravity is 9.8 m/s^2. We can calculate the mass of the man using the formula:
Weight = Mass * Acceleration due to gravity on Earth
Rearranging the formula, we have:
Mass = Weight / Acceleration due to gravity on Earth
Let's calculate the mass of the man on Earth first:
Mass = 1220 N / 9.8 m/s^2
≈ 124.49 kg
Now, using the mass of the man and the free-fall acceleration on Jupiter (25.9 m/s^2), we can calculate his weight on Jupiter:
Weight on Jupiter = Mass * Acceleration due to gravity on Jupiter
Weight on Jupiter = 124.49 kg * 25.9 m/s^2
≈ 3,222.71 N
Therefore, the man would weigh approximately 3,222.71 N on Jupiter.
To determine the man's weight on Jupiter, we need to use the equation:
Weight = mass × acceleration due to gravity.
However, we don't know the mass of the man. Since mass does not change when the gravitational acceleration changes, we can use the fact that weight is directly proportional to the acceleration due to gravity.
Let's calculate the mass of the man on Earth first using the equation:
Weight on Earth = mass × acceleration due to gravity on Earth.
Rearranging the equation:
mass = Weight on Earth / acceleration due to gravity on Earth
mass = 1220 N / 9.8 m/s^2
mass ≈ 124.49 kg (rounded to two decimal places)
Now, we can calculate the weight of the man on Jupiter:
Weight on Jupiter = mass × acceleration due to gravity on Jupiter
Weight on Jupiter = 124.49 kg × 25.9 m/s^2
Weight on Jupiter ≈ 3,221.15 N (rounded to two decimal places)
Therefore, the man would weigh approximately 3,221.15 N on Jupiter.