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salantis [7]
3 years ago
11

A 15g bullet is fired horizontally into a 3kg block of wood suspended by a long cord. Assume that the bullet remains in the bloc

k and that it swings 0.086m above the initial height. Calculate the velocity of the bullet when it strikes the wood.
Physics
1 answer:
Varvara68 [4.7K]3 years ago
5 0

Answer:

261.3 m/s

Explanation:

Mass of bullet=m=15 g=\frac{15}{1000}=0.015 kg

1 kg=1000g

Mass of block=M=3 kg

d=0.086 m

Total mass =M+m=3+0.015=3.015 kg

K.E at the time strike=Gravitational potential energy at the end of swing

\frac{1}{2}(m+M)^2V^2=(m+M)gh

Using g=9.8m/s^2

Substitute the values

\frac{1}{2}(3.015)V^2=3.015\times 9.8\times 0.086

V^2=\frac{2\times 3.015\times 9.8\times 0.086}{3.015}

V=\sqrt{2\times 3.015\times 9.8\times 0.086}}

V=1.3m/s

Velocity after collision=V=1.3 m/s

Velocity of block=v'=0

Using conservation law of momentum

mv+Mv'=(m+M)V

Using the formula

0.015v+3(0)=3.015(1.3)

0.015v=3.015(1.3)

v^2=\frac{3.015(1.3)}{0.015}=261.3

v=261.3 m/s

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For what absolute value of the phase angle does a source deliver 71 % of the maximum possible power to an RLC circuit
kherson [118]

Answer: the absolute value of the phase angle is 28°

Explanation:

taking a look at expression for the instantaneous electric power in an AC circuit;

P = VI -------let this be equation 1

p is power, v is voltage and I is current;

for maximum power

P_max = V_rms × I_rms --------let this be equ 2

where P_max is the maximum power, V_rms is the rms value of voltage and I_rms is the rms value of current.

Also for average electric power in an AC circuit

P_avg = V_rms × I_rms × cos²∅ -------let this be equ 3

where P_avg is the average power and cos∅ is the power factor

now from equation 2;  P_max = V_rms × I_rms

so p_max replaces V_rms × I_rms in equation 3

we now have

P_avg = P_max × cos²∅

so we substitute

expression for the given value of the average power is

P_avg = P_max × 75%

p_avg = P_max.78/100

for the expression of the average electricity in an AC circuit

P_max.78/100 = P_max × cos²∅

78/100 = cos²∅

to get the absolute value of phase angle

∅ = cos⁻¹ ( √(78/100))

∅ =  cos⁻¹ ( 0.8832)

∅ = 27.969 ≈ 28°

Therefore the absolute value of the phase angle is 28°

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Answer

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Although these quantities vary from one type of cell to another, a cell can be 1.9 μm in diameter with a cell wall 60 nm thick.
DaniilM [7]

Answer: 2(10)^{-9} mg

Explanation:

We know the total diameter of the cell (assumed spherical) is:

d=1.9\mu m=1.9(10)^{-6} m

Then its total radius r=\frac{d}{2}=\frac{1.9(10)^{-6} m}{2}=9.5(10)^{-7} m

On the other hand, we know the thickness of the cell wall is r_{t}=60 nm= 60(10)^{-9} m and its density is the same as water (\rho=997 kg/m^{3}).

Since density is the relation between the mass m and the volume V:

\rho=\frac{m}{V}

The mass is: m=\rho V (1)

Now if we are talking about this cell as a thin spherical shell, its volume will be:

V=\frac{4}{3}\pi R^{3} (2)

Where  R=r-r_{w}=9.5(10)^{-7} m - 60(10)^{-9} m

Then:

V=\frac{4}{3}\pi (9.5(10)^{-7} m - 60(10)^{-9} m)^{3} (3)

V=2.952(10)^{-18} m^{3} (4)

Substituting (4) in (1):

m=(997 kg/m^{3})(2.952(10)^{-18} m^{3}) (5)

m=2.94(10)^{-15} kg (6)

Knowing 1 kg=1000 g and 1 mg=0.001 g:

m=2.94(10)^{-15} kg=2(10)^{-9} mg

7 0
3 years ago
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