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: work = 1,305kJ
Explanation:
angle= 30°
force= 1,500N
distance= 1,000m
The formula for work is : Work= force x distance, however there is an angle of 30° between the direction of force applied and the direction of motion, therefore force must be decomposed to its value on the horizontal axis which is the direction of motion by using the cosine of the very angle.
W= F×cos(α)×D
W= 1,500×cos (30)×1,000
W= 1,305kJ ( kilojoules)
The velocity at the maximum height will always be 0. Therefore, you will count your final velocity as 0, and your initial velocity as 35 m/s. Next, we know that the acceleration will be 9.8 m/s^2. How? Because the ball is thrown directly upward, and the only force acting on it will be the force of gravity pushing it back down.
The formula we use is h = (Vf^2 - Vi^2) / (2*-9.8m/s^2)
Plugging everything in, we have h = (0-1225)/(19.6) = 62.5 meters is the maximum height.
Answer:
position as a function of time is y = 0.05 × cos(9.9)t
Explanation:
given data
mass = 5 kg
length = 10 cm = 0.1 m
displaced = 5 cm
to find out
position as a function of time
solution
we will apply here equilibrium that is
mass × g = k × length
put here value and find k
k = 
k = 490 N/m
and ω is
ω = 
ω = 
ω = 9.9
so here position w.r.t time is
y = 0.05 × cosωt
y = 0.05 × cos(9.9)t
so position as a function of time is y = 0.05 × cos(9.9)t
Answer:
f=m*a
Explanation:
The formula for force says force is equal to mass (m) multiplied by acceleration (a)
