Answer:
YFy = 0 = Ffsinθ + Fncosθ - Fw
Explanation:
From the base of the vector Fn, draw a vertical line. the small angle between this line and Fn is also theta. The component of Fn in the vertical direction is Fncos(theta).
Take a moment to picture extreme cases. Sine is 0 at 0 and 1 at 90. Cosine is 1 at 0 and 0 at 90.
Tilt the incline so that the box is on a flat surface. How much of the gravitational force is along the x direction of the floor.
Answer:
![F_f=840N](https://tex.z-dn.net/?f=F_f%3D840N)
Explanation:
From the question we are told that
Weight of fireman ![W_f= 87.5kg](https://tex.z-dn.net/?f=W_f%3D%2087.5kg)
Pole distance ![D=4.10m](https://tex.z-dn.net/?f=D%3D4.10m)
Final speed is ![V_f 1.75m/s](https://tex.z-dn.net/?f=V_f%201.75m%2Fs)
Generally the equation for velocity is mathematically represented as
![v^2 = v_0^2 + 2 a d](https://tex.z-dn.net/?f=v%5E2%20%3D%20v_0%5E2%20%2B%202%20a%20d)
Therefore Acceleration a
Generally the equation for Frictional force
is mathematically given as
![F_f=m*a](https://tex.z-dn.net/?f=F_f%3Dm%2Aa)
![F_f=m*(g-0.21)](https://tex.z-dn.net/?f=F_f%3Dm%2A%28g-0.21%29)
![F_f=87.5*(9.81-0.21)](https://tex.z-dn.net/?f=F_f%3D87.5%2A%289.81-0.21%29)
Therefore
![F_f=840N](https://tex.z-dn.net/?f=F_f%3D840N)
Answer:
time required after impact for a puck is 2.18 seconds
Explanation:
given data
mass = 30 g = 0.03 kg
diameter = 100 mm = 0.1 m
thick = 0.1 mm = 1 ×
m
dynamic viscosity = 1.75 ×
Ns/m²
air temperature = 15°C
to find out
time required after impact for a puck to lose 10%
solution
we know velocity varies here 0 to v
we consider here initial velocity = v
so final velocity = 0.9v
so change in velocity is du = v
and clearance dy = h
and shear stress acting on surface is here express as
= µ ![\frac{du}{dy}](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdy%7D)
so
= µ
............1
put here value
= 1.75×
× ![\frac{v}{10^{-4}}](https://tex.z-dn.net/?f=%5Cfrac%7Bv%7D%7B10%5E%7B-4%7D%7D)
= 0.175 v
and
area between air and puck is given by
Area =
area =
area = 7.85 ×
m²
so
force on puck is express as
Force = × area
force = 0.175 v × 7.85 × ![10^{-3}](https://tex.z-dn.net/?f=10%5E%7B-3%7D)
force = 1.374 ×
v
and now apply newton second law
force = mass × acceleration
- force = ![mass \frac{dv}{dt}](https://tex.z-dn.net/?f=mass%20%5Cfrac%7Bdv%7D%7Bdt%7D)
- 1.374 ×
v = ![0.03 \frac{0.9v - v }{t}](https://tex.z-dn.net/?f=0.03%20%5Cfrac%7B0.9v%20-%20v%20%7D%7Bt%7D)
t = ![\frac{0.1 v * 0.03}{1.37*10^{-3} v}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1%20v%20%2A%200.03%7D%7B1.37%2A10%5E%7B-3%7D%20v%7D)
time = 2.18
so time required after impact for a puck is 2.18 seconds
Answer:
29.38 seconds
Explanation:
Half life, T = 22.07 s
No = 1293
Let N be the number of atoms left after time t
N = 1293 - 779 = 514
By the use of law of radioactivity
![N=N_{0}e^{-\lambda t}](https://tex.z-dn.net/?f=N%3DN_%7B0%7De%5E%7B-%5Clambda%20t%7D)
Where, λ is the decay constant
λ = 0.6931 / T = 0.6931 / 22.07 = 0.0314 decay per second
so,
![514=1293e^{-0.0314t}](https://tex.z-dn.net/?f=514%3D1293e%5E%7B-0.0314t%7D)
![2.5155=e^{0.0314t}](https://tex.z-dn.net/?f=2.5155%3De%5E%7B0.0314t%7D)
take natural log on both the sides
0.9225 = 0.0314 t
t = 29.38 seconds
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