I will name block a as Ma=5 kg, block b as Mb=10 kg and mass of the pulley M=3 kg and radius as R. Since the system will accelerate in the direction of the block b because it has greater mass, I will take that direction as positive. Both blocks and the pulley have the same acceleration because the slipping on the pulley is neglected. First, the equations of motion:
Mb*g-Tg=MbαR and
Ta-Ma*g=MaαR,
where Ta and Tb are the tensions of the cord, g=9.81 m/s^2 and α is the angular accereration. Also a=αR where a is the acceleration of the system.
Now the equation of rotational dynamics of a solid body:
(Tb-Ta)R=Iα=(1/2)*M*R^2*α, where (1/2)*M*R^2 is the moment of inertia of a disc.
When we input Tb=Mb*g - Mb*α*R and Ta=Ma*g + Ma*α*R from the first two equations into the third we get: (Mb*g - Mb*α*R - Ma*α*R - Ma*g)*R=(1/2)*M*R^2*α.
We solve for α and get: α=(Mb*g-Ma*g)/((1/2)*MR+Mb*R+Ma*R)=2.97 rad/s^2.
We know that a=α*R and we easily get a=0.4455 m/s^2
There is no definite end to earths atmosphere, but technically the border between the outer space and earth gets thinner as you move up from the earths surface. The Karman line is the closest definition there is which describes the end of the earth's atmosphere, it is 100 km above earth's sea level at approximately 1.56 % of total earth's radius. This describes the boundary between the outer space and the atmosphere.
Extinct<span> might be a word you associate with animals that lived long ago, like the dinosaurs, but did you know that over 18,000 species are classified as "threatened" (susceptible to extinction) today? Scientists involved in wildlife conservation have a tough job; they are in charge of determining what needs to be done to prevent a species from becoming extinct. Habitat, food supply, and impacts of local human populations are just a few of the factors these scientists take into account. It is a lot to keep track of for a single location, but the job becomes even harder when it is a migratory animal. In this science project, you will get a firsthand look at their job. You will access </span>real<span> data about migratory birds and use satellite images to analyze their habitats, then come up with a conservation plan to protect the species from extinction.</span>
initial velocity=0m/s
acceleration=4.2m/s^2
time taken =5s
then final velocity
v=u+at
or, v=0+4.2*5
so final velocity is 21m/s
Frequency with wavelength 1.162m<span> = 344/1.162 = 296.04</span><span>Hz</span>