EIAT Mechanical Flashcards

As seen in the illustration, three identically sized balls made of the materials K, L, and M are floating in the water. The items are being acted upon by buoyant forces FK, FL, and FM. Which of the aforementioned statements about these forces is true?

Answer: Fb (K) > Fb (M) > Fb (L)

By Archimedes' principle, a floating object's buoyant force equals its own weight, which equals the weight of the water it displaces. Since the three balls are the same size but made of different materials, the densest (heaviest) ball sinks deepest and displaces the most water, giving it the largest buoyant force — so the order is K > M > L. The forces aren't equal because the balls have different weights.

Which way does the grey wheel rotate? (Mark C if neither.)

Answer: A

Explanation: A linear velocity changes to an angular velocity when the rack (toothed belt) comes into contact with the cogwheels. The point of contact's location is crucial. The lower portion of the red cogwheel is where it comes into contact with the rack. The linear velocity to the right is induced by the counterclockwise angular velocity. The upper portion of the grey cogwheel is where it comes into contact with the rack. The rack-determined linear velocity to the right causes a clockwise-moving angular velocity.

What are the differences between gear 3's rotational direction and speed (angular velocity) and gear 1's?

Answer: Gear 3 rotates slower than gear 1 and both rotate in the same direction

Connected through an idler gear (gear 2), gears 1 and 3 turn in the same direction. Because gear 3 is the larger gear, the gear ratio makes it rotate slower than gear 1. So gear 3 is both slower and turning the same way — not equal in speed and not opposite in direction.

A 40cm spring suspended on a hook 1.2m above the ground has a constant 2000 N/m force. At the spring's low point, a solid sphere with a 5 cm radius is suspended. What is the solid sphere's maximum weight without touching the ground?

Answer: 1400 N

The spring's bottom sits 0.8 m above the ground (1.2 m hook height − 0.4 m spring length), and the sphere's 0.1 m diameter must clear the floor, leaving a maximum stretch of 0.7 m. By Hooke's law, F = kx = 2000 × 0.7 = 1400 N, the heaviest the sphere can be. Larger weights would stretch the spring enough for the sphere to touch the ground.

There is a whistle from a railroad. 5 seconds later, there is an echo. How far away is the reflecting surface if the speed of sound is 343 m/s?

Answer: 857.5 m

An echo is a round trip: the sound travels to the reflecting surface and back, all within the 5 seconds. The total path is 343 × 5 = 1715 m, so the one-way distance to the surface is half of that, 857.5 m. The 1715 m option forgets to halve the round-trip distance.

A 24 cm converging lens is 12 cm away from an object that is 10 cm high. How high is the image this lens creates?

Answer: 20 cm

Using the thin lens equation 1/f = 1/do + 1/di with f = 24 cm and do = 12 cm gives di = −24 cm, so the magnification M = −di/do = 2. The image height is M × object height = 2 × 10 = 20 cm. The image is twice as tall as the object, so 10 cm or 5 cm undercount the magnification.

Which way is the wheel going to turn? (Mark C if neither.)

Answer: B

Explanation: The leftmost two wheels are connected by a band. The band moves in response to the clockwise rotation of the bottom wheel (blue arrow), which in turn causes the top wheel to rotate counterclockwise. The band is crossed, which is why. Due to the rod connecting the two wheels at the top, they both rotate in the same direction. The aforementioned wheel will rotate counterclockwise because it is connected by a straight band to the wheel at the top right.