Answer:
w = 4,786 rad / s
, f = 0.76176 Hz
Explanation:
For this problem let's use the concept of angular momentum
L = I w
The system is formed by the two discs, during the impact the system remains isolated, we have the forces are internal, this implies that the external torque is zero and the angular momentum is conserved
Initial Before sticking
L₀ = 0 + I₂ w₂
Final after coupling
= (I₁ + I₂) w
The moments of inertia of a disk with an axis of rotation in its center are
I = ½ M R²
How the moment is preserved
L₀ =
I₂ w₂ = (I₁ + I₂) w
w = w₂ I₂ / (I₁ + I₂)
Let's reduce the units to the SI System
d₁ = 60 cm = 0.60 m
d₂ = 40 cm = 0.40 m
f₂ = 200 min-1 (1 min / 60 s) = 3.33 Hz
Angular velocity and frequency are related.
w₂ = 2 π f₂
w₂ = 2π 3.33
w₂ = 20.94 rad / s
Let's replace
w = w₂ (½ M₂ R₂²) / (½ M₁ R₁² + ½ M₂ R₂²)
w = w₂ M₂ R₂² / (M₁ R₁² + M₂ R₂²)
Let's calculate
w = 20.94 8 0.40² / (12 0.60² + 8 0.40²)
w = 20.94 1.28 / 5.6
w = 4,786 rad / s
Angular velocity and frequency are related.
w = 2π f
f = w / 2π
f = 4.786 / 2π
f = 0.76176 Hz
Answer:
Answer:
6.68 x 10^16 m/s^2
Explanation:
Electric field, E = 3.8 x 10^5 N/C
charge of electron, q = 1.6 x 10^-19 C
mass of electron, m = 9.1 x 10^-31 kg
Let a be the acceleration of the electron.
The force due to electric field on electron is
F = q E
where q be the charge of electron and E be the electric field
F = 1.6 x 10^-19 x 3.8 x 10^5
F = 6.08 x 10^-14 N
According to Newton's second law
Force = mass x acceleration
6.08 x 10^-14 = 9.1 x 10^-31 x a
a = 6.68 x 10^16 m/s^2
Explanation:
The height at time t is given by
h(t) = -4.91t² + 34.3t + 1
When the ball reaches maximum height, its derivative, h'(t) = 0.
That is,
-2(4.91)t+34.3 = 0
-9.82t + 34.3 = 0
t = 3.4929 s
Note that h''(t) = -9.82 (negative) which confirms that h will be maximum.
The maximum height is
hmax = -4.91(3.4929)² + 34.3(3.4929) + 1
= 60.903 m
Answer:
The ball attains maximum height in 3.5 s (nearest tenth).
The ball attains a maximum height of 60.9 m (nearest tenth)
Answer:
Part a)
Part b)
Explanation:
Diameter of the circle = 24 ft
Diameter = 731.52 cm = 7.3152 m
now the horse complete 144 trips in one hour
so time to complete one trip is given as
now the speed of the horse is given as
Part a)
Now we know that the power is defined as rate of work done
it is given as
Part b)
Work done to climb up to 3 m height is given by
now we have
now we know that 1 HP = 746 Watt
so we have