Mastering Bennett Mechanical Comprehension Problems: A Deep Dive

What is the rotation velocity and direction of wheel C if wheel A makes 30 rot/min and RA = 3RB and RC = 2RB?

• A. 15 rot/min
• B. 60 rot/min
• C. 45 rot/min
• D. 30 rot/min

Answer: (C)

To determine the rotation velocity and direction of wheel C, we first need to establish the relationship between the wheels based on their radii and the given rotation speed of wheel A. It is provided that wheel A rotates at 30 rotations per minute (rot/min) and has a radius (RA) that is 3 times the radius of wheel B (RB). Therefore, we can express this relationship as RA = 3RB. Wheel C has a radius (RC) that is 2 times the radius of wheel B (RB), or RC = 2RB. When comparing the rotation speeds of connected wheels, the principle of conservation of energy must be upheld. The linear speeds of the edges of connected wheels must be equal. The linear speed (v) of the edge of a wheel is calculated using the formula: v = rot/min × radius For wheel A: v_A = 30 rot/min × RA For wheel B, since RA = 3RB: v_B = (30 rot/min × 3RB) = 90RB Since wheel B connects to wheel C, we use the relationship of their radii to find the rotation speed of wheel C. The linear speed must also equal the linear speed of wheel

When it comes to preparing for the Bennett Mechanical Comprehension Test, understanding the relationship between rotating objects—like wheels—is crucial. So, let's break down a problem related to wheels A, B, and C that illustrates some of the fundamentals you’ll encounter. Sounds interesting, right? It might feel like a puzzle at first, but once you grasp the mechanics, it’ll all click into place.

Imagine wheel A rotating at 30 rotations per minute (rot/min). Now, here's the catch: its radius (RA) is three times that of wheel B (RB). So, RA = 3RB. Pretty straightforward, huh? Now, wheel C connects to wheel B but with a radius (RC) that is two times that of wheel B. It helps to visualize it—like if your bicycle's front wheel is super big and the back wheel is smaller, but both are essential for getting where you want to go!

Now, let’s explore how to figure out the rotation velocity and direction of wheel C. The key here is remembering a crucial principle from physics: the conservation of energy. The linear speeds at the edges of wheels connected to each other must be equal.

Here's the formula: v = rot/min × radius.

For wheel A:

[ v_A = 30 \text{ rot/min} \times RA ]

Given that RA is three times RB:

[ v_A = 30 \text{ rot/min} \times 3RB = 90RB ]

Now, onto wheel B’s linear speed:

[ v_B = 90RB ]

The cool part? Since wheel B is connected to wheel C, we can use its relationship to find out wheel C’s rotation speed. Remember, we established earlier that RC = 2RB. This means C will rotate faster based on its smaller radius, so we want to find the rotation speed using the linear speed equations.

Since ( v_E ) of wheel C matches ( v_B ):

[ v_C = rot_C \times RC ]

[ rot_C \times (2RB) = 90RB ]

By simplifying that, we can solve for rotation speed (rot_C):

[ rot_C = \frac{90RB}{2RB} = 45 \text{ rot/min} ]

And voilà! That means wheel C rotates at 45 rot/min. Isn’t that an exciting breakthrough? It's all about understanding the relationships and the formulas behind the scenes.

Mastering problems like these is not just about rote memorization; it's about developing a mindset that lets you see how everything connects. Whether you're considering careers in mechanical engineering, manufacturing, or any technical field, a solid grasp of these principles not only prepares you for tests like the Bennett but also gives you an edge in real-world applications.

By practicing problems thoroughly, understanding how to apply the principles we just discussed, and recognizing how different components in mechanical systems interact, you'll develop the confidence you need to ace your upcoming tests. Who knows? With a bit of practice, you might just find yourself helping others solve similar puzzles in the future. So, gear up, and let's get rolling—because mastering mechanical comprehension can truly unlock doors for you ahead.