Answer:
The fastest object is the sphere, so it is the winner
Explanation:
To know which object will arrive faster down, let's look for the velocity of the center of mass of each object. Let's use the concept of mechanical energy
Highest point
Em₀ = U = mg y
Lowest point
= K = + = ½ I w² + ½ m ²
Angular velocity is related to linear velocity.
v = w r
w = v / r
= ½ I ²/r² + ½ m ²
= ½ (I / r² + m) ²
Energy is conserved
Em₀ =
mg y = ½ (I / r² + m) ²
= √2 g y / (I / mr² +1)
With this expression we can know which object arrives as a higher speed, therefore invests less time and is the winner. Let's calculate the speed of the center of mass of each
Ring
I = m r²
= √ (2 g y / (m r² / mr² + 1))
= √ (2gy 1/2)
= (√ 2gy) 0.707
Solid sphere
I = 2/5 m r²
= √ (2gy / (2/5 m r² / mr² + 1)
= √ (2gy / (7/5))
= √ (2gy 5/7)
= (√ 2gy) 0.845
Cylinder
I = ½ m r²
= √ (2gy / ½ mr² / mr² + 1)
= √ (2gy / (3/2))
= √ (2g y 2/3)
= (√ 2gy) 0.816
The fastest object is the sphere, so it is the winner when descending the ramp
Answer:
2. Letter C all those in the list are non living
3. Letter A a skunk is a living organism that shapes its environment
5. Letter A when talking about population it usually refers to a single type of species in that area
6. Letter B Niche (just recently heard of the word in ecology)