The Rocket Club is planning to launch a pair of model rockets. To build the rocket, the club needs a rocket body paired with an engine. The table lists the mass of three possible rocket bodies and the force generated by three possible engines.
| Body | Mass (kg) | Engine | Force (N) |
|---|---|---|---|
| 1 | 0.500 | 1 | 25 |
| 2 | 1.5 | 2 | 20 |
| 3 | 0.750 | 3 | 30 |
Based on Newton's laws of motion, which combination of rocket bodies and engines will result in the acceleration of 40 [tex]$m / s ^2$[/tex] at the start of the launch?
A. Body 3 + Engine 1
B. Body 2 + Engine 2
C. Body 1 + Engine 2
D. Body 1 + Engine 1
Answer (1)
Calculate the acceleration for each combination using a = F / m .
Combination 1 (Body 3 + Engine 1): a = 25/0.75 = 33.33 m / s 2 .
Combination 2 (Body 2 + Engine 2): a = 20/1.5 = 13.33 m / s 2 .
Combination 3 (Body 1 + Engine 2): a = 20/0.5 = 40 m / s 2 .
Combination 4 (Body 1 + Engine 1): a = 25/0.5 = 50 m / s 2 . The combination that results in 40 m / s 2 is Body 1 + Engine 2, so the answer is B o d y 1 + E n g in e 2 .
Explanation
Understanding the Problem We are given the mass of three rocket bodies and the force generated by three engines. We need to find the combination of rocket body and engine that results in an acceleration of 40 m / s 2 . We will use Newton's second law of motion, which states that Force (F) = mass (m) × acceleration (a), or a = F/m.
Calculating Acceleration for Each Combination We will calculate the acceleration for each of the four given combinations:
Body 3 + Engine 1: Mass = 0.750 kg, Force = 25 N a 1 = m F = 0.750 k g 25 N = 33.33 m / s 2
Body 2 + Engine 2: Mass = 1.5 kg, Force = 20 N a 2 = m F = 1.5 k g 20 N = 13.33 m / s 2
Body 1 + Engine 2: Mass = 0.500 kg, Force = 20 N a 3 = m F = 0.500 k g 20 N = 40 m / s 2
Body 1 + Engine 1: Mass = 0.500 kg, Force = 25 N a 4 = m F = 0.500 k g 25 N = 50 m / s 2
Finding the Correct Combination Comparing the calculated accelerations with the target acceleration of 40 m / s 2 , we find that:
Combination 1: 33.33 m / s 2
Combination 2: 13.33 m / s 2
Combination 3: 40 m / s 2
Combination 4: 50 m / s 2
Only Combination 3 (Body 1 + Engine 2) results in the desired acceleration of 40 m / s 2 .
Final Answer Therefore, the combination of rocket body and engine that will result in an acceleration of 40 m / s 2 at the start of the launch is Body 1 + Engine 2.
Examples
Newton's laws of motion are fundamental in physics and engineering. For example, when designing a car, engineers use these laws to calculate the engine's required force to achieve a specific acceleration, considering the car's mass. Similarly, in sports, understanding these principles helps athletes optimize their performance, such as calculating the force needed to throw a ball at a certain speed or the angle at which to kick a ball to maximize its range. These calculations ensure designs meet performance requirements and athletes can achieve their desired outcomes.
