Answer:
Explanation:
Given
average speed of train![(v_{avg})=216 kmph\approx 60 m/s](https://tex.z-dn.net/?f=%28v_%7Bavg%7D%29%3D216%20kmph%5Capprox%2060%20m%2Fs)
Maximum acceleration=0.05g
Now centripetal acceleration is
![a_c=\frac{v^2}{r}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7Bv%5E2%7D%7Br%7D)
![0.05\times 9.8=\frac{60^2}{r}](https://tex.z-dn.net/?f=0.05%5Ctimes%209.8%3D%5Cfrac%7B60%5E2%7D%7Br%7D)
r=7346.93 m
(b)Radius of curvature=900 m
therefore ![a_c=\frac{v^2}{r}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7Bv%5E2%7D%7Br%7D)
![v=\sqrt{a_cr}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7Ba_cr%7D)
![v=\sqrt{0.05\times 9.8\times 900}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B0.05%5Ctimes%209.8%5Ctimes%20900%7D)
![v=\sqrt{441}=21 m/s](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B441%7D%3D21%20m%2Fs)
The work done by a rotating object can be calculated by the formula Work = Torque * angle.
This is analog to the work done by the linear motion where torque is analog to force and angle is analog to distance. This is Work = Force * distance.
An example will help you. Say that you want to calculate the work made by an engine that rotates a propeller with a torque of 1000 Newton*meter over 50 revolution.
The formula is Work = torque * angle.
Torque = 1000 N*m
Angle = [50 revolutions] * [2π radians/revolution] = 100π radians
=> Work = [1000 N*m] * [100π radians] = 100000π Joules ≈ 314159 Joules of work.
<h2>
Answer: x=125m, y=48.308m</h2>
Explanation:
This situation is a good example of the projectile motion or parabolic motion, in which we have two components: x-component and y-component. Being their main equations to find the position as follows:
x-component:
(1)
Where:
is the projectile's initial speed
is the angle
is the time since the projectile is launched until it strikes the target
is the final horizontal position of the projectile (the value we want to find)
y-component:
(2)
Where:
is the initial height of the projectile (we are told it was launched at ground level)
is the final height of the projectile (the value we want to find)
is the acceleration due gravity
Having this clear, let's begin with x (1):
(3)
(4) This is the horizontal final position of the projectile
For y (2):
(5)
(6) This is the vertical final position of the projectile
Refer to the diagram shown below.
Let I = the moment of inertia of the wheel.
α = 0.81 rad/s², the angular acceleration
r = 0.33 m, the radius of the weel
F = 260 N, the applied tangential force
The applied torque is
T = F*r
= (260 N)*(0.33 m)
= 85.8 N-m
By definition,
T = I*α
Therefore,
I = T/α
= (85.8 N-m)/(0.81 rad/s²)
= 105.93 kg-m²
Answer: 105.93 kg-m²
Answer:
v = 12.86 km/h
v = 3.6 m/s
Explanation:
Given,
The distance, d = 13.5 km
The time, t = 21/20 h
= 1.05 h
The velocity of a body is defined as the distance traveled by the time taken.
v = d / t
= 13.5 km / 1.05 h
= 12.86 km/h
The conversion of km/h to m/s
1 km/h = 0.28 m/s
12.86 km/h = 12.86 x 0.28 m/s
= 3.6 m/s
Hence, the velocity in m/s is, v = 3.6 m/s