The table shows the acceleration due to gravity on four different planets. What planet is a person standing on if the person has a mass of 85.0 kg and weighs 305 N?
a
Venus
b
Mars
c
Mercury
d
Earth
The weight of a person is given by the formula: Weight = mass * acceleration due to gravity.
To determine which planet the person is standing on, we need to compare the weight of the person to the weight they would have on each planet.
On Earth, the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the person on Earth is:
Weight = mass * acceleration due to gravity
Weight = 85.0 kg * 9.8 m/s^2
Weight = 833 N
Since the person weighs 305 N, we can conclude that they are not on Earth.
Now, let's compare the weight of the person to the weights they would have on the other planets.
On Venus, the acceleration due to gravity is approximately 8.87 m/s^2. Therefore, the weight of the person on Venus is:
Weight = mass * acceleration due to gravity
Weight = 85.0 kg * 8.87 m/s^2
Weight ≈ 753 N
On Mars, the acceleration due to gravity is approximately 3.71 m/s^2. Therefore, the weight of the person on Mars is:
Weight = mass * acceleration due to gravity
Weight = 85.0 kg * 3.71 m/s^2
Weight ≈ 315 N
On Mercury, the acceleration due to gravity is approximately 3.7 m/s^2. Therefore, the weight of the person on Mercury is:
Weight = mass * acceleration due to gravity
Weight = 85.0 kg * 3.7 m/s^2
Weight ≈ 315 N
Comparing the weights, we can see that the person weighs 305 N, which closely aligns with the weight on Mars. Therefore, the person is standing on Mars (option b).