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Apple
Mechanical Engineer was asked...July 14, 2009

You put a glass of water on a record turntable and begin slowly increasing the speed. What happens first - does the glass slide off, tip over, or does the water splash out.

7 Answers

I was asked this question in separate interviews by Apple, then later by Lab126 (Amazon). I got the answer correct, and they told me so. This question evaluates candidates intuitive sense (engineering judgment) about how things behave when subject to multiple forces, including visualizing free body diagrams and understanding how multiple forces can be resolved into resultant forces (and their angles) to predict how a body moves. The conceptual answer is: this problem can be understood by considering a sufficiently small fluid element at the surface of the water in the glass. That tiny sub-volume of water experiences two forces: 1) gravitational force pulling down on that small mass of water; 2) the force of centripetal acceleration acting upon that small mass of water. When viewed in the (rotating) reference frame of that tiny volume of water under study, the centripetal force is a side-acting force and the gravitational is downward acting. The surface of the water will change to a shape that is NORMAL to the resultant vector of those two forces. Holding rotational freq constant, the water angle will get steeper as its radial location on the record player increases, because the centripetal force is proportional to radius multiplied by the SQUARE of the angular frequency. It can be shown that the water will take on the shape of a sub-portion of the surface of a PARABOLA centered with its minima at the center axis of the record player. As the angular frequency increases, the glass will either slide, or it will tip over, and which of these depends on the aspect ratio of the glass (position of COG) and the friction between the glass and the record player. Some water could splash out prior to either of those events, if the glass was nearly filled with water before the water angle started to change when the turntable started spinning Downward acting gravitational force: F = m X g Side acting centripetal force: F= (omega^2) X r, where omega is angular freq in rad/s If THETA = the tangential angle of the water relative to the plane of the record player, then: TAN (Theta) = (omega^2) r / g Interviewers often give major credit if candidate can at least get CONCEPTUAL answer correct. Less

Depends on several factors including where the glass is placed (the outer edge will experience stronger forces) and how much water is in the glass (I think). Less

The above description is largely correct except this "It can be shown that the water will take on the shape of a sub-portion of the surface of a PARABOLA centered with its minima at the center axis of the record player." This is true only if the glass is placed at the center of the record player..in all other cases the shape will not be the same due to the effect of centripetal force acting on just direction (as opposed to uniform/all direction in the case of rotating glass at the center) Less

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Apple

A car on a hill of constant slope accelerates from rest under gravity to a point on the hill. If you want to maximize the velocity of the car at this point, where along the length of the car (e.g. downhill or uphill) would you fix an additional mass, if (a) the finishing point is on the slope of the hill or (b) the finishing point is on a flat below the slope of the hill.

5 Answers

i wan to add another thing, if you consider friction, the more heavier you are the more friction you will encounter because weight is proportional to friction and you will be slower vs lighter weight. Less

This is effectively a conservation of energy question: a) Fixing an additional mass is sort of arbitrary. The delta of the height would be the same, so it doesn't matter. If you don't have to fix it, things change. Think about it and it'll come... b) Back. No question. You capitalize on the potential energy of the center of mass for longer. The front of the car will be at h=0 while the back is still at h=h0 right at the transition point. You'll really need to understand it to give a good answer, though. Good luck... Less

You put it in the back (or more specifically, behind the car), but not so far that when the car makes the transition the angular acceleration lets the car get up on it's rear wheels, resulting in the weight hitting the ground and having dragging friction. Less

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Apple

What kind of job do you want

4 Answers

I answered with wrong direction

What kind of job are you offering me?

i need mechanical engineer job

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Apple

If you have a diving board that is three body lengths long, 1 inch thick and shoulder width wide what dimension should you reduce if you want to decrease deflection the most for the least change?

3 Answers

Length

the thickness is the smallest value of L * w * h doubling the h, will yield 8x less deflection Less

Change the cross section from rectangle to a "T" or a "W"

Apple

Deformation of beams: how would beam bolted together would behave vs beam stacked on each other. I could not figure the equation out instantaneously but he asked to find the answer the same day and e-mail him. I did found the answer and e-mail the manager..

3 Answers

It is related to shear stress in beams. when you develop equations for Shear stress in a beam, we use this analogy to account for the presence of longitudinal shear stress in the beam. You can solve it through equations but I think they are looking for if you can explain the difference in behaviour Less

The question is more focused on parallel and series beam question. For the parallel beam ( for your case 2 beams stacked on top of each other) the total deflection will be same. And for the beams in series ( bolted beams together in your case) the total deflection will the summation of individual deflection of the beams Less

look up standard beam deflection formula and solve it

Apple

You are on a boat on a lake. There is a large rock with with you on a boat. If you push the rock into the lake, would water level rise, stay same or decrease? Explain your answer.

2 Answers

It will decrease. Apply Achimedes' principle.

Archimedes' principle

Apple

- You have a bowling ball in a boat then you drop it off the side and it sinks to the bottom. Will the water in the pool rise or fall? - You have two bowling balls that are identical on the outside and weigh the same on the top of an inclined ramp. One is hollow and one is solid. You let both of them roll down the ramp. Which one will reach the bottom first? - How would you reduce the deflection of a simply supported beam? - A pinned beam supported by a line that has an apple logo hanging from it. How would you reduce the stress in the line? - Lots of questions about how I used data analysis to make design decisions in my projects in my portfolio. - You have a 5 gallon jug and a 3 gallon jug and a hose that supplies endless water. You want to put 4 gallons in the 5 gallon jug. How can you put 4 gallons in the 5 gallon jug? (not an apple interview question but figured it might be helpful)

2 Answers

For the last question, I would first fill up the 3 gal jug to the brim and then transfer all of the water to the 5 gallon jug. Then I would again fill up the 3 gallon jug and transfer as much water as possible to the 5 gallon jug. Once this is done, the 5 gallon jug will be full and the 3 gallon jug will be left with 1 gallon of water. I would then throw away all the water in the 5 gallon jug, and fill it with the 1 gal of water currently left in the 3 gal jug. Then I would again fill up the 3 gal jug to the brim and transfer all of its water into the 5 gal jug which already has 1 gal of water- thus giving me a total of 4 gals of water in the 5 gallon jug Less

1. The water in the pool will drop. When you have the bowling ball in the boat, the amount of water displaced is equal to the mass of the bowling ball divided by the density of water. When the bowling ball sinks, the amount of water displaced is equal to the volume of the bowling ball, which is the mass of the bowling ball divided by the density of the bowling ball. Since the question states that the bowling ball sinks to the bottom, the density of the bowling ball > density of the water. Thus, less water is displaced when the bowling ball is dropped into the water. This means that the water level will drop. 2. The solid one will reach the bottom first assuming you let both of them roll at the same time. Classical physics problem concerning conservation of energy. Key is to learn that kinetic energy is split into rotational and translational. In this case, since the solid object has a small moment of inertia, it requires less rotational kinetic energy and can travel faster. 3. Use the standard formula: deflection = (Moment * Beam Length) / (c * E * I). c is some constant, E is young's modulus and I is moment of inertia. Decrease moment and beam length. Increase Young's modulus and I. 4. You can increase the cross sectional area of that line or reduce the weight of the logo. Less

Apple

Between the following materials, steel, magnesium, titanium, copper, aluminum, which is the most stiff and why? What does the stress strain plot look like for steel versus aluminum? What should you do if you want to increase the force until fracture? What would the stress strain plot look like if you took a material went until ultimate strength and then went back to zero stress and then went back to ultimate strength?

2 Answers

The answer is steel

Steel has the highest stiffness as defined by the Young’s modulus.

Apple

If you are in a boat with a boulder and you drop that boulder into the lake how does the water level before and after you drop the boulder in the lake compar?

2 Answers

Assuming the boat is floating on the surface and the boulder sinks like a rock (its density is greater than that of water), then the water level should go down. When in the boat, the boulder caused the boat to displace the boulder's weight of water. Afterward, the boat displaces that much less and the boulder only displaces its volume of water, so the total displacement of water has decreased. Less

You need to prove mathematically why the level is constant.

Apple

What is the relation between strain and stress?

2 Answers

The relationship between stress and strain can be used to find many properties of a material, including ultimate tensile stress, yield elongation point, offset yield strength, and young's modulus. Young's Modulus (E) is actually the measurement of stress over strain. Stress is force over area, while strain is the deformation of the material in relationship to that stress. Less

Stress : when a force is applied that cause change in a physical body. Strain :Change in shape of a physical body on which stress is applied. Stress Stress is the force that can cause strain in an object. Strain:Strain is an object’s response to stress. Stress :Stress can be measured. Strain :Strain cannot be measured. Less

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