Bennett Mechanical Structures and Center of Gravity Questions and Answers 1 — Questions and Answers
Question 1: Four objects are made of the same uniform material. Which object is the most stable and least likely to tip over if placed on a flat, level surface?
- A tall, thin cylinder standing on its end
- A short, wide cone resting on its base (Correct answer)
- A perfect sphere
- A tall pyramid balanced on its point
Correct answer: A short, wide cone resting on its base
Stability is determined by two main factors: a low center of gravity and a wide base of support. [2, 5, 8] The short, wide cone has the lowest center of gravity and the widest base relative to its height, making it the most stable of the options. [8]
Question 2: A perfect 'L' shape is created by joining two identical, uniform rectangular blocks of wood at their ends. Where is the center of gravity of the combined 'L' shape located?
- Exactly at the point where the two blocks are joined.
- In the geometric center of the vertical block.
- In the geometric center of the horizontal block.
- In the empty space inside the 'corner' of the L. (Correct answer)
Correct answer: In the empty space inside the 'corner' of the L.
The center of gravity is the average position of all the mass in the object. For a composite, non-convex shape like an 'L', the balance point is not within the physical material of either individual block but is located in the open space formed by the corner. [22]
Question 3: Which of the following geometric shapes, when constructed with beams of equal length and joined by pins at its vertices, forms the most rigid structural element?
- A square
- A pentagon
- A triangle (Correct answer)
- A rectangle
Correct answer: A triangle
A triangle is an inherently rigid shape. [7, 9] Once its side lengths are fixed, its angles cannot change, preventing deformation under stress. Other shapes like squares or rectangles can easily be deformed into parallelograms without changing their side lengths. [3, 9] This is why triangles are fundamental to truss design in bridges and buildings. [7, 14]
Question 4: To ensure maximum stability and prevent rolling over during a sharp turn, where should a single, heavy crate be placed on the flatbed of a truck?
- As low and as close to the center of the truck bed as possible. (Correct answer)
- As far forward as possible, against the cab, and stacked high.
- On one side, directly over the rear wheels.
- As far back as possible on the tailgate.
Correct answer: As low and as close to the center of the truck bed as possible.
Placing heavy items low and centered keeps the vehicle's overall center of gravity low and balanced. [1, 19] A low center of gravity increases stability and reduces the likelihood of tipping during turns or on uneven roads. [5, 10, 13, 19]
Question 5: A horizontal cantilever beam is securely fixed into a wall at one end and extends outwards. If a heavy weight is hung from the free end, where will the beam experience the greatest bending stress?
- At the free end, where the weight is attached.
- Exactly in the middle of its length.
- At the point where it is fixed to the wall. (Correct answer)
- The stress is uniform along the entire length.
Correct answer: At the point where it is fixed to the wall.
The point where the beam is fixed to the wall must support the entire weight plus the turning force (moment) created by the weight acting at a distance. This results in the maximum bending moment and therefore the greatest stress at the fixed support. [21, 26]
Question 6: A tall, rectangular box is placed on a flat plank. The plank is then slowly tilted. At which point will the box begin to tip over?
- When the angle of the plank exceeds 45 degrees.
- When the top corner of the box is higher than the bottom corner.
- When the force of friction is no longer great enough to prevent sliding.
- When a vertical line drawn downward from the box's center of gravity falls outside its base of support. (Correct answer)
Correct answer: When a vertical line drawn downward from the box's center of gravity falls outside its base of support.
An object on an incline is stable as long as the vertical line extending from its center of gravity passes through its base of support. [2, 20] The moment the line falls outside the base, a tipping torque is created by gravity, and the object will overturn. [20, 28] Sliding occurs if the force of friction is overcome first, but the question asks about the condition for tipping. [27]
