# Math Help - 6 more... physics problems

1. ## 6 more... physics problems

1.) Two dams form artificial lakes of equal depth. However, one lake backs up 15 km behind the dam, and the other backs up 30 km behind. What effect does the difference in length have on the pressures on the dams?
a) The pressure from the shorter lake will be 1/2 that of the longer lake.
b) The pressurew from the shorter lake will be 1/4 that of the longer lake.
c) The pressure from the two will be the same.
d) The pressure from the longer lake will be 1/2 that of the shorter lake.
e) The pressure difference will depend on the actual depths.

2.) An ice cube floats in a glass of water. As the ice melts, the level of the water in the glass will:
a) Increase b) Decrease c) Stay the same.

3.) If the distance to a source is halved, how will the sound intensity level change?
a) Increase by a factor of 2.
b)Increase by a factor of 4.
c) Increase by 3 dB.
d) Increase by 6 dB.
e) depends on the acutal distance.

4.) Consider two slabs of material with the same thickness, but made of materials differing in their index of refraction. Which of the following are true?
a) Light incident at an angle from the normal will reflect off the two slabs are different angles.
b) Light incident normally will refract at different angles in the two slabs.
c) The speed of light will differ in the two slabs.
d) The frequency of light will differ in the two slabs.
e) The wavelength of light will be the same in the two slabs.

5.) Concrete is sold by the cubic yard. What is the mass, in kilograms, of one cubic yard of concrete that is five times as dense as water? (1.000 m = 1.094 yd, and 1.000 m $^3$) of water has a mass of 1.000 x 10 $^3$ kg.)
a) 764 kg b) 6546 kg c) 3819 kg d) 8733 kg e) 2420 kg

6.) A piece of iron sinks to the bottom of a lake where the pressure is 21 atm. Which statement best describes what happens to the density of that piece of iron?
a) Its density decreases slightly.
b)Its density increases slightly.
c) Its density becomes 21 times greater.
d) There has been no change in the density of the iron.

2. Originally Posted by John 5
1.) Two dams form artificial lakes of equal depth. However, one lake backs up 15 km behind the dam, and the other backs up 30 km behind. What effect does the difference in length have on the pressures on the dams?
a) The pressure from the shorter lake will be 1/2 that of the longer lake.
b) The pressurew from the shorter lake will be 1/4 that of the longer lake.
c) The pressure from the two will be the same.
d) The pressure from the longer lake will be 1/2 that of the shorter lake.
e) The pressure difference will depend on the actual depths.
Pressure in a perfect fluid depends only on the depth of the fluid. ( $P = \rho g d$, where $\rho$ is the density of the fluid.) Thus the answer is e).

Originally Posted by John 5
2.) An ice cube floats in a glass of water. As the ice melts, the level of the water in the glass will:
a) Increase b) Decrease c) Stay the same.
The volume of water displaced by the ice cube is the same as the volume of ice submerged. BUT ice is less dense than water. So the melting ice expands. Thus the water level will go up (very slightly).

Originally Posted by John 5
3.) If the distance to a source is halved, how will the sound intensity level change?
a) Increase by a factor of 2.
b)Increase by a factor of 4.
c) Increase by 3 dB.
d) Increase by 6 dB.
e) depends on the acutal distance.
Sound intensity is an "areal" law, that is to say intensity depends on the amount of area the wave covers at a certain distance from the source. (I = P/A, where I is intensity, P is the power of the source, and A is the area.) Sound waves are spherical in nature so the area goes as $r^2$ (r being the distance from the source.) So as we are halving r the intensity increases by
$\frac{1}{\left ( \frac{1}{2} \right )^2} = 4$, so the answer is b).

-Dan

3. Originally Posted by John 5
4.) Consider two slabs of material with the same thickness, but made of materials differing in their index of refraction. Which of the following are true?
a) Light incident at an angle from the normal will reflect off the two slabs are different angles.
b) Light incident normally will refract at different angles in the two slabs.
c) The speed of light will differ in the two slabs.
d) The frequency of light will differ in the two slabs.
e) The wavelength of light will be the same in the two slabs.
a) No. If it has an (real) index of refraction it will refract light, not reflect it.
b) Yes, see my comment on a).
c) Yes, the speed of light in a material depends on the index of refraction of that material: $c^{\prime} = c/n$, where c is the speed of light, n is the index of refraction, and c' is the speed of light in the material.
d) Yes. The frequency of the light does not change as we pass from one material to another.
e) No. The wavelength of the light will depend on the index of refraction.

Originally Posted by John 5
5.) Concrete is sold by the cubic yard. What is the mass, in kilograms, of one cubic yard of concrete that is five times as dense as water? (1.000 m = 1.094 yd, and 1.000 m $^3$) of water has a mass of 1.000 x 10 $^3$ kg.)
a) 764 kg b) 6546 kg c) 3819 kg d) 8733 kg e) 2420 kg
You can do this! 1 kg of water has a volume of what? Well, the density of water is $1 ~g/cm^3$:
$\frac{1~g}{1~cm^3} \cdot \frac{1~kg}{1000~g} \cdot \left ( \frac{100~cm}{1~m} \right )^3 \cdot \left ( \frac{1.000~m}{1.094~yd} \right )^3 = 463.744~kg/yd^3$

Concrete is 5 times this dense, so...

Originally Posted by John 5
6.) A piece of iron sinks to the bottom of a lake where the pressure is 21 atm. Which statement best describes what happens to the density of that piece of iron?
a) Its density decreases slightly.
b)Its density increases slightly.
c) Its density becomes 21 times greater.
d) There has been no change in the density of the iron.
Technically the surface of a metal is slightly malleable, so the answer is b). However on the practical side I must note that 21 atm probably isn't going to deform iron by all that much. I'm not an expert but the density change may not even be measurable. In light of this I would go with answer d) rather than b), but speak to your instructor about it.

-Dan

4. Originally Posted by topsquark
...

The volume of water displaced by the ice cube is the same as the volume of ice submerged. BUT ice is less dense than water. So the melting ice expands. Thus the water level will go up (very slightly).

...
Hello,

I'm a little bit confused. I believed that the weight of the fluid which is displaced by a floating solid has the same value as the weight of the solid itself (Archimedes's principle). That means the ice-cube displaces as much water as it contains. Thus the level of the fluid will stay the same.

Was I wrong?

5. Originally Posted by earboth
Hello,

I'm a little bit confused. I believed that the weight of the fluid which is displaced by a floating solid has the same value as the weight of the solid itself (Archimedes's principle). That means the ice-cube displaces as much water as it contains. Thus the level of the fluid will stay the same.

Was I wrong?
The weight of the displaced fluid has a value equal to the bouyant force on the object. (And hence is directly related to the masses.) See here for much more detail. I was referring to the volume of displaced water vs. the volume of the ice submerged, which will be the same for both.

Grrr.. I may have, in fact, answered this wrong but I have to rush off. Someone else please double check me and apologies if I was wrong!

-Dan

6. ## couple of problems im confused about

13) Sound vibrations with frequencies greater than 20,000 Hz are called?
a)infrasonics
b)supersonics
c)ultrasonics
d)megasonics

14) The lowest tone to resonate in an open pipe of length L is 400 Hz. what is the frequency of the lowest tone that will resonate in a closed pipe of length 2L.
a)100Hz
b)0.800kHz
c)200Hz
d)1.60kHz

15) For certain angles, TOTAL INTERNAL REFLECTION can occur when light tries to pass from one medium to another which has.
a)a larger index of refraction
b)a smaller index of refraction
c)an index of refraction which is sin(45 degrees)
d)an index of refraction which is sin-1(Θ)
e)the same index of refraction

16) A ray of light, which is traveling in air, is incident on a glass plate at a 45 degrees angle. The most we can say about the angle of refraction in the glass.
a) is less than 45 degrees
b)is equal to 45 degrees
c)is unknown because it all depends on the index of refraction of glass
d)is greater than 45 degrees

17) An index of refraction less than one for a medium would imply that.
a)the speed of light in the medium is greater than the speed of light in vacuum.
b)the speed of light in the medium is the same as the speed of light in vacuum.
c)refraction is not possible
d)reflection is not possible

18) which of the following materials has the slowest speed of light?
a)water
b)oil
c)air
d)flint glass