The hoop is attached.
Consider that the friction force is given by:
F = μ·N
= μ·m·g·cosθ
We also know, considering the forces of the whole system, that:
F = -m·a + m·g·sinθ
and
a = (1/2)·<span>g·sinθ
Therefore:
</span>-(1/2)·m·g·sinθ + m·g·sinθ = <span>μ·m·g·cosθ
</span>(1/2)·m·g·sinθ = <span>μ·m·g·cosθ
</span>μ = (1/2)·m·g·sinθ / <span>m·g·cosθ
= </span>(1/2)·tanθ
Now, solve for θ:
θ = tan⁻¹(2·μ)
= tan⁻¹(2·0.9)
= 61°
Therefore, the maximum angle <span>you could ride down without worrying about skidding is
61°.</span>
Answer: there are 15 coins of $2 and 18 coins of $5
Explanation:
I will answer in English.
X is the number of $5 coins.
Y is the number of $2 coins.
We have the system of equations:
Y + X = 33
Y*2 + X*5 = 120
first, we must isolate one of the variables in one of the equations and then replace it in the other equation, let's isolate Y in the first equation:
Y = 33 - X.
Then we can replace it in the other equation:
(33 - X)*2 + X*5 = 120
66 - X*2 + X*5 = 120
X*3 = 54
X = 54/3 = 18
and using the equation for Y.
Y = 33 - X = 33 - 18 = 15
So there are 15 coins of $2 and 18 coins of $5
Answer:
The formula to calculate velocity in this case:
v = v0 + at
=> a = (v - v0)/t
= (50 - 0)/4
= 50/4 = 12.5 (m/s2)
Hope this helps!
:)
(a) According to Newton’s third law, for every action
there is an equal yet opposite reaction. In this case, the cannonball is
affected by 8.0x10^3 newtons in one direction. Now the cannon must also be
affected by the same amount of net force on the opposite direction.
- 8.0x10^3 Newtons (the negative symbol only shows that it
is opposite direction)
(b) We solve this using the formula:
F = m a
8.0x10^3 N = (1.0 kg) a
a = 8,000 m/s^2
Answer:
The angle is 
Explanation:
From the question we are told that
The distance of separation is 
The wavelength of light is 
Generally the condition for destructive interference is mathematically represented as
![dsin(\theta ) =[m + \frac{1}{2} ]\lambda](https://tex.z-dn.net/?f=dsin%28%5Ctheta%20%29%20%20%3D%5Bm%20%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20%5D%5Clambda)
Here m is the order of maxima, first minimum (dark space) m = 0
So
![100 *10^{-6 } * sin(\theta ) =[0 + \frac{1}{2} ]600 *10^{-9}](https://tex.z-dn.net/?f=100%20%2A10%5E%7B-6%20%7D%20%2A%20%20sin%28%5Ctheta%20%29%20%20%3D%5B0%20%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20%5D600%20%2A10%5E%7B-9%7D)
=> ![\theta = sin^{-1} [0.003]](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%20sin%5E%7B-1%7D%20%5B0.003%5D)
=> 