Suppose a rocket launches with an acceleration of 32.0m/s^2.

What is the apparent weight of an 95-kg astronaut aboard this rocket?

Taking g=9.81m/s^2

The astronaut will experience normal weight (due to gravity) plus weight due to acceleration.

Apparent weight = 95kg * (1+32.0/9.81)

The force experienced is: 95 *(9.81+32.0) N

Graham is correct; I just do not like the way that it is explained in some examples solved. I saw this earlier, but left it alone, and went and did something else.

The resultant force points up and you have the force of gravity point down subtracting from the weight. So the resultant force is the weight of the astronaut minus the the gravitational force.

ΣF=ma=W-Fg

ma=W-Fg

(95kg)*(32.0m/s^2)=Fw-95kg*(9.8m/s^2)

Solving for Fw,

Fw=(95kg)*(32.0m/s^2)+(95kg)*(9.8m/s^2)

Fw=95kg(32.0m/s^2+9.8m/s^2)

Solve

Graham and I are in agreement; I just explained differently.

To find the apparent weight of the astronaut, we need to consider the gravitational force and the acceleration due to the rocket's motion. The apparent weight is the force experienced by the astronaut.

Step 1: Calculate the gravitational force:
The gravitational force experienced by the astronaut can be calculated using the formula:

F_gravity = mass * acceleration due to gravity

F_gravity = 95 kg * 9.8 m/s^2 (acceleration due to gravity is approximately 9.8 m/s^2)

F_gravity = 931 N

Step 2: Calculate the net force:
The net force experienced by the astronaut consists of the gravitational force (opposite direction) and the force due to the rocket's acceleration (in the direction of acceleration).

Net force = F_gravity + F_rocket

Net force = F_gravity + (mass * acceleration)

Net force = 931 N + (95 kg * 32.0 m/s^2)

Step 3: Calculate the apparent weight:
The apparent weight is the magnitude of the net force experienced by the astronaut.

Apparent weight = |Net force|

Apparent weight = |931 N + (95 kg * 32.0 m/s^2)|

Apparent weight = |931 N + 3040 N|

Apparent weight = |3971 N|

Therefore, the apparent weight of the 95-kg astronaut aboard the rocket is 3971 N.

To calculate the apparent weight of an astronaut aboard the rocket, you need to consider the acceleration, mass of the astronaut, and the force of gravity acting on the astronaut.

The apparent weight of an object is the force exerted by a surface to support the weight of the object. It is equal to the normal force exerted by the surface on the object.

Here are the steps to calculate the apparent weight:

Step 1: Calculate the force of gravity acting on the astronaut using the formula:

Force of gravity = mass × acceleration due to gravity

The acceleration due to gravity on Earth is approximately 9.8 m/s^2.

∴ Force of gravity = mass × 9.8

For a 95-kg astronaut, the force of gravity would be:

Force of gravity = 95 kg × 9.8 m/s^2

Step 2: Calculate the net force acting on the astronaut using Newton's second law of motion:

Net force = mass × acceleration

In this case, the acceleration is the acceleration of the rocket, given as 32.0 m/s^2.

∴ Net force = 95 kg × 32.0 m/s^2

Step 3: Calculate the apparent weight using the equation:

Apparent weight = Force of gravity - Net force

Substitute the values calculated in Steps 1 and 2 into the equation:

Apparent weight = (95 kg × 9.8 m/s^2) - (95 kg × 32.0 m/s^2)

Simplifying this equation will give you the apparent weight of the astronaut aboard the rocket.