A 50-kg astronaut experiences an acceleration of 5.0g (up) during liftoff. What is the astronaut's true weight and apparent weight?
for anyone's future reference...
mg = mass * acceleration due to gravity
in this case (50 kg * 9.81 m/s^2) + (50 kg * 49.05 m/s^2) = 2943 N, 3000 N with sig figs
[5.0 g = 5.0 * 9.81 m/s^2]
To find the true weight and apparent weight of the astronaut, we need to understand the concept of weight and apparent weight.
Weight is the force with which a body is attracted towards the center of the Earth due to gravity. It can be calculated using the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s².
Apparent weight, on the other hand, is the force exerted by a supporting surface on an object.
In this case, the astronaut is experiencing an acceleration of 5.0g (up) during liftoff. One g is equal to the acceleration due to gravity on Earth, so 5.0g means five times the acceleration due to gravity.
Let's calculate the true weight and apparent weight of the astronaut:
1. Calculate the true weight:
True Weight = mass × acceleration due to gravity
True Weight = 50 kg × 9.8 m/s²
True Weight = 490 N
Therefore, the true weight of the astronaut is 490 Newtons.
2. Calculate the apparent weight:
Apparent Weight = mass × net acceleration
Net acceleration = acceleration due to gravity + acceleration during liftoff
Acceleration during liftoff = 5.0g × acceleration due to gravity
Acceleration during liftoff = 5.0 × 9.8 m/s² = 49 m/s²
Net acceleration = acceleration due to gravity + acceleration during liftoff
Net acceleration = 9.8 m/s² + 49 m/s² = 58.8 m/s²
Apparent Weight = 50 kg × 58.8 m/s²
Apparent Weight = 2940 N
Therefore, the apparent weight of the astronaut is 2940 Newtons.
true weight: mg
apparentweigh: mg+ma