Answer:
Mass of the ring is 2.5 kg.
Given:
Moment of inertia of a ring = 0.4 kg.
Radius = 40 cm = 0.4 m
To find:
Mass of the ring = ?
Formula used:
I = m
Where I = moment of inertia
r = radius of the ring
m = mass of the ring
Solution:
Moment of inertia of a ring is given by,
I = m
Where I = moment of inertia
r = radius of the ring
m = mass of the ring
0.4 = m ×0.4×0.4
m = 0.4/(0.4×0.4)
m = 1/0.4
m = 2.5 kg
Mass of the ring is 2.5 kg.
Answer:
The decelerating force is
Solution:
As per the question:
Frontal Area, A =
Speed of the spaceship, v =
Mass density of dust,
Now, to calculate the average decelerating force exerted by the particle:
(1)
Volume,
Thus substituting the value of volume, V in eqn (1):
where
A = Area
v = velocity
t = time
(2)
From Newton's second law of motion:
Thus differentiating w.r.t time 't':
where
= average decelerating force of the particle
Now, substituting suitable values in the above eqn:
Answer:
v = 1.09*10^5 m/s
Explanation:
In order to calculate the speed of the proton when it reaches the negative plate, you first calculate the acceleration of the proton, produced by the electric force.
You use the second Newton law:
(1)
q: charge of the proton = 1.6*10^-19 C
m: mass of the proton = 1.67*10^-27 kg
E: magnitude of the electric field between the plates = 5.50*10^4N/C
You solve for the acceleration a in the equation (1):
Next, you use the following formula to find the final speed of the proton:
(2)
v: final speed of the proton = ?
vo: initial speed of the proton = 0m/s
x: distance traveled by the proton = 2.30mm/2 = 1.15mm = 1.15*10^-3m
You replace the values of all parameters in the equation (2):
The speed of the proton when it reaches the negative plate is 1.09*10^5 m/s
Ω = 2000 rpm, initial angular speed.
t = 30 s, the time for the wheel to come to rest.
Calculate the angular deceleration, α.
w - αt = 0
(209.4395 rad/s) - (α rad/s²)*(30 s) = 0
α = 6.9813 rad/s²
The angular distance traveled, θ, is given by
ω² - 2αθ = 0
θ = ω²/(2α)
= 209.4395²/(2*6.9813)
= 3141.6 rad
The number of revolutions is
3141.6/(2π) = 500
Answer: 500 revolutions