Answer:
29°
Explanation:
because the refracted ray angle is small than angle of incidence
Answer:
Explanation:
The gravitational potential at a point on the Earth surface is given by:
where
G=6.67×10^-11Nm^2kg^-2 is the gravitational constant
M=5.98×10^24kg is the Earth's mass
R=6.38×10^6 m is the Earth's radius
Substituting the numbers into the equation, we find
Answer:
B. If isolated from a eukaryotic cell, mitochondria can no longer survive and reproduce on their own.
Given Information:
Diameter of the cylindrical tub = d = 50 cm = 0.50 m
Acceleration = α = 3g
Required Information:
1. Rotation rate in rev/min = ω = ?
2. Tangential speed in m/s = v = ?
Answer:
1. ω = 103.5 rev/min
2. v = 2.71 m/s
Explanation:
We know that centripetal acceleration is given by
α = ω²r
Where ω is the angular speed or rotation rate and r is the radius.
The relation between diameter and radius is given by
r = D/2
r = 0.50/2
r = 0.25 m
Since it is given that the acceleration is equal to 3g where g is the gravitational acceleration 9.81 m/s².
α = ω²r
3g = ω²r
ω² = 3g/r
ω = √(3g/r)
ω = √(3*9.81/0.25)
ω = 10.84 rad/s
To convert rad/s into rev/s divide it by 2π
ω = 10.84/2π
ω = 1.752 rev/s
To convert rev/s into rev/min multiple it by 60
ω = 1.752*60
ω = 103.5 rev/min
Therefore, the rotation rate is 103.5 rev/min
2. The tangential speed can be found using
v = ωr
Where ω is the rotation rate in rad/s and r is the radius.
v = 10.84*0.25
v = 2.71 m/s
Therefore, the tangential speed is 2.71 m/s
Answer:
ΔX = 0.0483 m
Explanation:
Let's analyze the problem, the car oscillates in the direction y and advances with constant speed in the direction x
The car can be described with a spring mass system that is represented by the expression
y = A cos (wt + φ)
The speed can be found by derivatives
= dy / dt
= - A w sin (wt + φ
So that the amplitude is maximum without (wt + fi) = + -1
= A w
X axis
Let's reduce to the SI system
vₓ = 15 km / h (1000 m / 1 km) (1h / 3600s) = 4.17 m / s
As the car speed is constant
vₓ = d / t
t = d / v
ₓ
t = 4 / 4.17
t = 0.96 s
This is the time between running two maximums, which is equivalent to a full period
w = 2π f = 2π / T
w = 2π / 0.96
w = 6.545 rad / s
We have the angular velocity we can find the spring constant
w² = k / m
m = 1200 + 4 80
m = 1520 m
k = w² m
k = 6.545² 1520
k = 65112 N / m
Let's use Newton's second law
F - W = 0
F = W
k x = W
x = mg / k
Case 1 when loaded with people
x₁ = 1520 9.8 / 65112
x₁ = 0.22878 m
Case 2 when empty
x₂ = 1200 9.8 / 65112
x₂ = 0.18061 m
The height variation is
ΔX = x₁ -x₂
ΔX = 0.22878 - 0.18061
ΔX = 0.0483 m