Physics Problems

• Down in a deep coal mine, a mile or so below the surface of the earth, is the force of gravity more or less than that at the entrance to the mine up at ground level? (Assume the Earth has a uniform density, and ignore any centrifugal and centripetal forces).

Answer
Down a mineshaft, the gravitational effect would be less because there is less mass below you. For the more technically minded, whilst the gravity increases in an R-Squred relationship as you are getting closer to the centre of the earth, the mass is an R-cubed relationship, hence the effect of mass is the more dominant ( assuming uniform density, although density isn't uniform).

• A man holds a rifle horizontally 6 feet above the ground. At the moment he fires it, another bullet is dropped from the same height, 6 feet.

Ignoring frictional effects and the curvature of the earth, which bullet hits the ground first?

Answer
The bullets hit the ground at the same time. The rate at which the moving bullet falls is determined by the force of gravity. This force is vertical and entirely independent of the horizontal velocity of the projectile. Its vertical descent is the same regardless of any horizontal velocity it may have.

• Pour hot water into a thick drinking glass and into a thin wine glass. Which glass in more likely to crack? And why?

Answer
The thick glass is most likely to crack

• A ball, a disc and a ring, each 5 inches in diameter, sit at the top of an inclined plane. If all three objects start rolling down the incline at the same instant, which one will reach the bottom first? (Assume that they all roll efficiently that is, they are perfectly formed and don't wobble--and ignore any effect of air resistance and friction.)

Answer
The ball will reach the bottom first. Because it has less mass on the outside, and hence less inertia.

• The speed of sound in air is about 740 miles per hour. Suppose that a police car is sounding its siren and is driving towards you at 60 miles per hour. At what speed is the sound of the siren approaching you?

Answer
The speed of sound coming from a police siren is the same whether or not the siren is standing still or moving.

• Rupert is sailing a plastic boat in his bathtub. The boat is loaded with nuts, bolts and washers. If Rupert dumps all these items into the water. allowing his boat to float empty, will the water level in the bath rise or fall?

Answer
The level will fall:the metal in the boat forces the boat to sink lower in the water, displacing water not only for the bolts, but for the air in the hull at water level. if the bolts are allowed to sink, they displace less volume than they did in the boat(try it).

• It is generally accepted that matter expands with increasing temperature, and contracts with decreasing temperature. There is one notable exception. Which is it, and why has nature provided for it?

Answer
Water expands below 3.98°C down to 0°C Otherwise ice would be heavier than water, with catastrophic consequences. Lakes and ocean's would freeze from the bottom up killing all life.

• How could you make a raw egg float halfway between the surface and the bottom of a glass of water?

Answer
You float a raw egg by putting salt in the water until the density of the water equals that of the egg.

• An ice cube is floating in a beaker of water, with the entire system at 0º Centigrade(32ºF). Just enough heat is applied to melt the ice cube without raising the temperature of the system. What happens to the water level in the beaker? Does it rise, fall, or stay the same?

Answer
The water level neither rises nor falls: it stays the same. The reason an ice cube floats is because its volume has expanded during crystallisation.