Answer:
a) a = 0.477 m/s^2
b) u = 0.04862
Explanation:
Given:-
- The rotational speed of the turntable N = 33 rev/min
- The watermelon seed is r = 4.0 cm away from axis of rotation.
Find:-
(a) Calculate the acceleration of the seed, assuming that it does not slip. (b) What is the minimum value of the coefficient of static friction between the seed and the turntable if the seed is not to slip
Solution:-
- First determine the angular speed (w) of the turntable.
w = 2π*N / 60
w = 2π*33 / 60
w = 3.456 rad/s
- The watermelon seed undergoes a centripetal acceleration ( α ) defined by:
α = w^2 * r
α = 3.456^2 * 0.04
α = 0.477 m / s^2
- The minimum friction force (Ff) is proportional to the contact force of the seed.
- The weight (W) of the seed with mass m acts downwards. The contact force (N) can be determined from static condition of seed in vertical direction.
N - W = 0
N = W = m*g
- The friction force of the (Ff) is directed towards the center of axis of rotation, while the centripetal force acts in opposite direction. The frictional force Ff = u*N = u*m*g must be enough to match the centripetal force exerted by the turntable on the seed.
Ff = m*a
u*m*g = m*a
u = a / g
u = 0.477 / 9.81
u = 0.04862
Answer: 0.0138 m^2 = 138 cm^2
Explanation:
The thermal expansion is the term use for the physical phenomena of dilation of the objects when they are exposed to changes in temperature.
The objects dilate when they are heated and contract when they are cooled.
The dilation is proportional to the change in temperatur.
For linear dilation, the proportionality constant is called linear dilation coefficient of the materials, it is named α and is measured in °C ^-1.
ΔL = α * Lo * ΔT, which means that the dilation (or contraction) is proportional to the product of the original length (Lo) and the change of temperature (ΔT).
There is also superficial dilation, for which the dilation is:
ΔA = β * Ao * ΔT, which means that the superficial dilation (or contraction) is proportional to the product of the original area (Ao) and the change of temperature (ΔT).
It is very interesting and important to solve problems that β = 2α, because regularly you will find the values of α for different materials and so, you just to multiply it times 2 to use β.
For this problem:
- Original area, Ao = area of the flat roof at - 10°C = 2.0m * 3.0m = 6.0 m^2.
- α for aluminum = 24 * 10^ -6 °C^-1.
- ΔT = 38°C - (-10°C) = 48°C
So, ΔA = 6.0m^2 * (2 * 24*10^-6 °C&-1) * 48°C = 0.0138 m^2
And that is the area that should stick out in summer to fit the structure during cold winter nights.
You can pass that number to cm^2 to grasp better the idea of this size:
0.0138 m^2 * (100 cm)^2 / m^2 = 138 cm^2
One way that the world's ocean affects weather and climate is by playing an important role in keeping our planet warm. ... The ocean doesn't just store solar radiation; it also helps to distribute heat around the globe. When water molecules are heated, they exchange freely with the air in a process called evaporation.
PE = 0.5 × k × x²
PE potential Energy
k spring constant
x stretch/compression of the spring
Despite the risks, Human populations can be found near volcanoes. This can be associated with the availability of which natural resource?
- <em>Geothermal</em><em> </em><em>energy</em>
<u>Geothermal</u><u> </u><u>energy</u><u> </u><u>is</u><u> </u><u>the</u><u> </u><u>f</u><u>o</u><u>r</u><u>m</u><u> </u><u>of</u><u> </u><u>energy</u><u> </u><u>obtained</u><u> </u><u>from</u><u> </u><u>the</u><u> </u><u>heat</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>earth</u><u>.</u><u> </u><u>Near</u><u> </u><u>volcanoes</u><u> </u><u>the</u><u> </u><u>land</u><u> </u><u>is</u><u> </u><u>more</u><u> </u><u>hot</u><u> </u><u>compared</u><u> </u><u>to</u><u> </u><u>the</u><u> </u><u>normal</u><u> </u><u>areas</u><u>.</u><u> </u><u>So</u><u>,</u><u> </u><u>the</u><u> </u><u>heat</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>lava</u><u> </u><u>will</u><u> </u><u>help</u><u> </u><u>in</u><u> </u><u>producing</u><u> </u><u>Geothermal</u><u> </u><u>energy</u><u>.</u><u>.</u><u>.</u><u>~</u>