A rocket takes off from Earth's surface, accelerating straight up at 31.2 m/s2. Calculate the normal force (in N) acting on an astronaut of mass 85.9 kg, including his space suit. (Assume the rocket's initial motion parallel to the y-direction. Indicate the direction with the sign of your answer.)

N = 3522.759 N in the upward direction

Explanation:

acceleration of the rocket, a = 31.2 m/s²

mass of the astronaut, m = 85.9 kg

g = 9.81 m/s²

Since the rocket takes off from Earth's surface, it moves upward and the equation, according to the second law of motion, is given by:

N - mg = ma

N - (85.9*9.81) = (85.9 * 31.2)

N - 842.679 = 2680.08

N = 2680.08 + 842.679

N = 3522.759 N in the upward direction

Since the normal force is positive, it is in the upward direction.

The value of the normal force is 2680.08N in the negative y direction

Explanation:

According to Newton's second law of motion, Force = mass * acceleration

Note that rocket takes off from Earth's surface, accelerating straight up at 31.2 m/s2,

Since the rocket accelerates upwards, the acceleration will be negative, since rockets acts contrary to the law of gravity (it keeps going into space without coming down)

acceleration of the rocket = - 31.2m/s²

Mass of the astronaut = 85.9kg

Normal force acting on the astronaut = - 31.2 * 85.9kg

= - 2680.08N

The value of the normal force is 2680.08N in the negative y direction