Answer:
(a): a = 0.4m/s²
(b): α = 8 radians/s²
Explanation:
First we propose an equation to determine the linear acceleration and an equation to determine the space traveled in the ramp (5m):
a= (Vf-Vi)/t = (2m/s)/t
a: linear acceleration.
Vf: speed at the end of the ramp.
Vi: speed at the beginning of the ramp (zero).
d= (1/2)×a×t² = 5m
d: distance of the ramp (5m).
We replace the first equation in the second to determine the travel time on the ramp:
d = 5m = (1/2)×( (2m/s)/t)×t² = (1m/s)×t ⇒ t = 5s
And the linear acceleration will be:
a = (2m/s)/5s = 0.4m/s²
Now we determine the perimeter of the cylinder to know the linear distance traveled on the ramp in a revolution:
perimeter = π×diameter = π×0.1m = 0.3142m
To determine the angular acceleration we divide the linear acceleration by the radius of the cylinder:
α = (0.4m/s²)/(0.05m) = 8 radians/s²
α: angular aceleration.
The correct answer is matter. Matter is a physical substance, so it is that only option provided that can be broken down to the subatomic particle level.
Answer: Carbon 14 and Uranium 238 are not used together to determine fossil ages.
Explanation:
Carbon 14 with a half life of 5,700 years can only be used to date fossils of approximately 50,000 years. Most fossils are thought to be much older than 50,000 years. Also most fossils no longer contain any Carbon. The fossilized remains have been mineralized where the original organic material has been replaced and turned into stones containing no carbon.
Uranium 238 has a half life of 4.5 billion years. Uranium can be used to date the age of the earth. If 50% of pure uranium' is left in a sample the sample is assumed to be 4.5 billion years old.( This is assuming that the original sample was 100% uranium and no Uranium 238 has been eroded or lost in 4.5 billion years old. If a fossil has only 25 % of the Uranium 238 the sample has an estimated age of 3.2 Billion years. This would be the estimated age of the earliest life or formation of fossils.
Note no fossils contain Uranium 238. Uranium 238 is only found in igneous or volcanic rocks. So no fossils can be dated directly using U 238.
Because of the huge differences in the half lives of Carbon 14 and Uranium238 they cannot be used together. Carbon 14 can only be used to date fossils of a very recent age. Uranium 238 can only be used to date volcanic rocks of a very old age.
Answer:2.67kgm/s cube
Explanation: density = mass ÷ volume = 400 ÷ 150
Answer:
v_f = 3 m/s
Explanation:
From work energy theorem;
W = K_f - K_i
Where;
K_f is final kinetic energy
K_i is initial kinetic energy
W is work done
K_f = ½mv_f²
K_i = ½mv_i²
Where v_f and v_i are final and initial velocities respectively
Thus;
W = ½mv_f² - ½mv_i²
We are given;
W = 150 J
m = 60 kg
v_i = 2 m/s
Thus;
150 = ½×60(v_f² - 2²)
150 = 30(v_f² - 4)
(v_f² - 4) = 150/30
(v_f² - 4) = 5
v_f² = 5 + 4
v_f² = 9
v_f = √9
v_f = 3 m/s
