Answer:
r = 4.44 m
Explanation:
For this exercise we use the Archimedes principle, which states that the buoyant force is equal to the weight of the dislodged fluid
B = ρ g V
Now let's use Newton's equilibrium relationship
B - W = 0
B = W
The weight of the system is the weight of the man and his accessories (W₁) plus the material weight of the ball (W)
σ = W / A
W = σ A
The area of a sphere is
A = 4π r²
W = W₁ + σ 4π r²
The volume of a sphere is
V = 4/3 π r³
Let's replace
ρ g 4/3 π r³ = W₁ + σ 4π r²
If we use the ideal gas equation
P V = n RT
P = ρ RT
ρ = P / RT
P / RT g 4/3 π r³ - σ 4 π r² = W₁
r² 4π (P/3RT r - σ) = W₁
Let's replace the values
r² 4π (1.01 10⁵ / (3 8.314 (70 + 273)) r - 0.060) = 13000
r² (11.81 r -0.060) = 13000 / 4pi
r² (11.81 r - 0.060) = 1034.51
As the independent term is very small we can despise it, to find the solution
r = 4.44 m
Answer:
The centripetal force acting on the child is 39400.56 N.
Explanation:
Given:
Mass of the child is, 
Radius of the barrel is, 
Number of revolutions are, 
Time taken for 10 revolutions is, 
Therefore, the time period of the child is given as:

Now, angular velocity is related to time period as:

Now, centripetal force acting on the child is given as:

Therefore, the centripetal force acting on the child is 39400.56 N.
Answer:

Explanation:
We are given that
Initial velocity=u=18ft/s
Final velocity,v=38ft/s
Time=t=3 s
We have to find the average acceleration over that 3 s period.
We know that
Average acceleration,a=
Using the formula
Average acceleration,a=
Average acceleration,a=
Average acceleration,a=
Hence, the average acceleration=
Answer:
0.5 m
Explanation:
Givens:
ym1 = 2.5 mm
ym2 = 4.5 mm
Ф_1=π / 4
Ф_2=π / 2
We have 2 ways to solve this problem. The first one given that the 2 waves have the frequency then we know that the resultant wave amplitude is
Ym = (ym1 + ym2)cos(Ф_2/2)
By substitution we have
Ym= (0.025 + 0.045)cos(π/4) = 0.496 m
The second one is it treat them as Phasors where the phase between them is Ф_2=π / 2 Therefore
Ym^2=(ym1^2+ym2^2)
So we have Ym=√0.025^2+0.045^2
= 0.5 m
Answer:
Incomplete question
Check attachment for the given diagram
Explanation:
Given that,
Initial Velocity of drum
u=3m/s
Distance travelled before coming to rest is 6m
Since it comes to rest, then, the final velocity is 0m/s
v=3m/s
Using equation of motion to calculate the linear acceleration or tangential acceleration
v²=u²+2as
0²=3²+2×a×6
0=9+12a
12a=-9
Then, a=-9/12
a=-0.75m/s²
The negative sign shows that the cylinder is decelerating.
Then, a=0.75m/s²
So, using the relationship between linear acceleration and angular acceleration.
a=αr
Where
a is linear acceleration
α is angular acceleration
And r is radius
α=a/r
From the diagram r=250mm=0.25m
Then,
α=0.75/0.25
α =3rad/sec²
The angular acceleration is =3rad/s²
b. Time take to come to rest
Using equation of motion
v=u+at
0=3-0.75t
0.75t=3
Then, t=3/0.75
t=4 secs
The time take to come to rest is 4s