Find the initial accerleration of a rocket if the sstronauts on board experience eight times their normal weight during an initial vertical ascent. (Hint: In this exercise, the scale force is replaced by the normal force.)
To find the initial acceleration of the rocket, we need to consider the forces acting on the astronauts during the initial vertical ascent.
According to the given information, the astronauts experience eight times their normal weight. This means that the force exerted on them is eight times the force of gravity (8g), where g is the acceleration due to gravity.
We can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the difference between the force exerted on the astronauts (8g) and the force of gravity (mg), where m is the mass of the astronauts.
So we have the equation:
Net force = 8mg - mg
To calculate the acceleration, we divide both sides of the equation by the mass (m):
a = (8mg - mg) / m
Simplifying this equation:
a = 7g
Therefore, the initial acceleration of the rocket is 7 times the acceleration due to gravity (7g).