Suppose a rocket launches with an acceleration of 39 m/s2. What is the apparent weight of an 90 kg astronaut aboard this rocket?
aweigth= m(g+a)
To calculate the apparent weight of the astronaut aboard this rocket, we need to consider the gravitational force acting on the astronaut and the additional force due to the acceleration of the rocket.
Step 1: Calculate the gravitational force acting on the astronaut.
The gravitational force can be calculated using the formula:
F_gravity = mass × gravitational acceleration
Given:
Mass of the astronaut (m) = 90 kg
Gravitational acceleration (g) = 9.8 m/s^2 (approximate value on Earth)
Using the formula, we can calculate the gravitational force:
F_gravity = 90 kg × 9.8 m/s^2 = 882 N
Step 2: Calculate the additional force due to acceleration.
The additional force can be calculated using the formula:
F_additional = mass × acceleration
Given:
Acceleration of the rocket (a) = 39 m/s^2
Using the formula, we can calculate the additional force:
F_additional = 90 kg × 39 m/s^2 = 3510 N
Step 3: Calculate the apparent weight.
The apparent weight is the sum of the gravitational force and the additional force. The apparent weight can be calculated as:
Apparent weight = F_gravity + F_additional
Apparent weight = 882 N + 3510 N = 4392 N
Therefore, the apparent weight of the 90 kg astronaut aboard this rocket is 4392 N.