Final answer:
To calculate the normal force acting on an astronaut during a rocket launch, subtract the gravitational force from the force due to the rocket's acceleration. In this case, the normal force is +5553.46 N upwards.
Step-by-step explanation:
The question asks us to calculate the normal force acting on an astronaut with a mass of 84.9 kg, including his space suit, as a rocket takes off from Earth's surface with an acceleration of 75.2 m/s2. To find the normal force, we need to consider both the gravitational force (weight) acting downwards and the force due to the rocket's acceleration acting upwards.
First, we calculate the gravitational force (weight) using the equation Fgrav = m × g, where m is the mass of the astronaut and g is the acceleration due to gravity (9.8 m/s2 on Earth). The weight of the astronaut is therefore 84.9 kg × 9.8 m/s2 = 831.42 N acting downwards.
Next, we calculate the force due to the rocket's acceleration using the equation Facc = m × a, where a is the rocket's acceleration. For the astronaut, this force is 84.9 kg × 75.2 m/s2 = 6384.88 N acting upwards.
The normal force exerted by the rocket's seat on the astronaut is the net force acting upwards, which is Fnormal = Facc - Fgrav. Therefore, the normal force is 6384.88 N - 831.42 N = 5553.46 N upwards.
If we consider upwards as positive, then the normal force acting on the astronaut is +5553.46 N.