Question

Find the initial acceleration of a rocket if the astronauts 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.)

Answer 1

The initial acceleration of the rocket is 7 times the gravitational acceleration.

Step-by-step explanation:

To find the initial acceleration of the rocket, we need to use the concept of normal force. When astronauts experience eight times their normal weight, it means that the normal force acting on them is eight times their weight. The normal force is equal to the sum of the gravitational force and the force exerted by the rocket. Let's represent the rocket's initial acceleration as 'a', the mass of the astronauts as 'm', and the gravitational acceleration as 'g'.

1. The normal force is given by the equation: Normal Force = Weight + Force of the Rocket = mg + Force of the Rocket.
2. Since the astronauts experience eight times their normal weight, the normal force is equal to 8mg.
3. Equating the two, we have: 8mg = mg + Force of the Rocket.
4. Simplifying the equation, we get: 7mg = Force of the Rocket.
5. Using Newton's second law, Force = mass x acceleration, we can substitute the force with 7mg and rearrange the equation to solve for acceleration: 7mg = ma.
6. The mass 'm' cancels out, leaving us with the equation: 7g = a.

Therefore, the initial acceleration of the rocket is 7 times the gravitational acceleration.

Answer 2

The initial acceleration of the rocket is approximately 7 times the acceleration due to gravity (7g).

Step-by-step explanation:

When astronauts experience eight times their normal weight during the initial vertical ascent of a rocket, the situation involves a combination of gravitational and normal forces. The net force acting on the astronauts is the difference between the gravitational force (weight) and the normal force, which is eight times their usual weight.

According to Newton's second law (F = ma), where force equals mass times acceleration, the equation for acceleration (a) becomes a = (W - N) / m, where W is the weight and N is the normal force. In this case, with N being 8 times the weight, the formula simplifies to a = (W - 8W) / m = -7g. The negative sign signifies that the acceleration is in the opposite direction to the gravitational force.

In essence, the initial acceleration of the rocket is approximately 7 times the acceleration due to gravity (7g). This implies that the astronauts onboard are subjected to a force equivalent to 7 times Earth's gravitational pull. Such insights into the interplay of forces are crucial in understanding the dynamics of rocket launches and the physical experiences of astronauts during these events.