In order to leave the earth's orbit, a spacecraft must accelerate $1,000 m / s ^2$. What net force is required if the spacecraft has a mass of 100,000 kilograms?
The problem asks for the net force acting on a spacecraft given its mass and required acceleration to leave Earth's orbit. We are provided with the following data:
We use the given values in the formula for Newton's Second Law:
Substituting these into the formula:
\[F = 100,000 \, \text{kg} \cdot 1,000 \, \text{m/s}^2\]
Calculating the product:
\[F = 100,000,000 \, \text{kg} \cdot \text{m/s}^2\]
Since \(1 \, \text{kg} \cdot \text{m/s}^2\) is defined as one Newton (\(\text{N}\)), the net force is \(100,000,000 \, \text{N}\). This can also be written in scientific notation as \(1 \times 10^8 \, \text{N}\).
The net force required for the spacecraft to achieve the specified acceleration is \(100,000,000 \, \text{N}\), or \(10^8 \, \text{N}\). Therefore, the final answer is \(\boxed{10^8 \, \text{N}}\).
Understanding how force relates to mass and acceleration is fundamental to aerospace engineering. For example, when designing rocket engines, engineers must calculate the thrust (force) required to lift a rocket of a certain mass to a specific speed to escape the gravitational pull of a planet. This basic principle is used daily in everything from automotive safety tests—where forces acting on passengers during sudden deceleration are measured—to the construction of roller coasters, where designers must ensure the force exerted on riders stays within safe limits.