Answer:
The angular acceleration of the pencil<em> α = 17 rad·s⁻²</em>
Explanation:
Using Newton's second angular law or torque to find angular acceleration, we get the following expressions:
τ = I α (1)
W r = I α (2)
The weight is that the pencil has is,
sin 10 = r / (L/2)
r = L/2(sin(10))
The shape of the pencil can be approximated to be a cylinder that rotates on one end and therefore its moment of inertia will be:
I = 1/3 M L²
Thus,
mg(L / 2)sin(10) = (1/3 m L²)(α)
α(f) = 3/2(g) / Lsin(10)
α = 3/2(9.8) / 0.150sin(10)
<em> α = 17 rad·s⁻²</em>
Therefore, the angular acceleration of the pencil<em> </em>is<em> 17 rad·s⁻²</em>
Answer:
Force, |F| = 2100 N
Explanation:
It is given that,
Water from a fire hose is directed horizontally against at a rate of 50.0 kg/s, 
Initial speed, v = 42 m/s
The momentum is reduced to zero, final speed, v = 0
The relation between the force and the momentum is given by :



|F| = 2100 N
So, the magnitude of the force exerted on the wall is 2100 N. Hence, this is the required solution.
Answer:
Temperature increase = 2.1 [C]
Explanation:
We need to identify the initial data of the problem.
v = velocity of the copper sphere = 40 [m/s]
Cp = heat capacity = 387 [J/kg*C]
The most important data given is the fact that when the shock occurs kinetic energy is transformed into thermal energy, therefore it will have to be:
![E_{k}=Q\\ E_{k}= kinetic energy [J]\\Q=thermal energy [J]\\Re-employment values and equalizing equations\\\\\frac{1}{2} *m*v^{2}=m*C_{p}*dT \\The masses are canceled \\\\dT=\frac{v^{2}}{C_{p} *2} \\dT=2.1 [C]](https://tex.z-dn.net/?f=E_%7Bk%7D%3DQ%5C%5C%20E_%7Bk%7D%3D%20kinetic%20energy%20%5BJ%5D%5C%5CQ%3Dthermal%20energy%20%5BJ%5D%5C%5CRe-employment%20values%20and%20equalizing%20equations%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%3Dm%2AC_%7Bp%7D%2AdT%20%20%5C%5CThe%20masses%20are%20canceled%20%5C%5C%5C%5CdT%3D%5Cfrac%7Bv%5E%7B2%7D%7D%7BC_%7Bp%7D%20%2A2%7D%20%5C%5CdT%3D2.1%20%5BC%5D)
Answer:
Explanation:
1. We use the conservation of momentum for before the raining and after. And also we take into account that in 0.5h the accumulated water is
100kg/h*0.5h = 50kg

2. the momentum does not conserve because the drag force of water makes that the boat loses velocity
3. If we assume that the force of the boat before the raining is

where we have assumed that the acceleration of the boat is 1m/s{2} just before the rain starts
And if we take the net force as

where we take v=1m/s because we are taking into account tha velocity just after the rain stars.
I hope this is useful for you
regards
<span>A "White" colored light must be shown by a 14-foot boat that is operating under oars after it is dark, in order to prevent a collision.
Boats which are less than 23 feet cannot exceed a maximum speed of 7 knots. They need to exhibit an all-around white light when it is sailing in the dark.
The other practicable sidelights can also be used instead of the white lights, when they are sailing in international waters.
</span>