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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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Darya [45]

Answer : The correct option is, (D) A machine does 400 joules of work in 5 seconds.

Explanation :

Power : It is defined a the rate of doing work per unit time.

Formula used :

P=\frac{w}{t}

where,

P = power

w = work done

t = time

Now we have to determine the rate of power for the following options.

(A) A machine does 200 joules of work in 10 seconds.

P=\frac{200}{10}=20W

(B) A machine does 400 joules of work in 10 seconds.

 P=\frac{400}{10}=40W

(C) A machine does 200 joules of work in 5 seconds.

 P=\frac{200}{5}=40W

(D) A machine does 400 joules of work in 5 seconds.

P=\frac{400}{5}=80W

From this we conclude that, a machine does 400 joules of work in 5 seconds has the highest rate of power.

Hence, the correct option is, (D)

8 0
3 years ago
The equation of a transverse wave traveling along a very long string is y 6.0 sin(0.020px 4.0pt), where x and y are expressed in
zhannawk [14.2K]

Answer:

given

y=6.0sin(0.020px + 4.0pt)

the general wave equation moving in the positive directionis

y(x,t) = ymsin(kx -?t)

a) the amplitude is

ym = 6.0cm

b)

we have the angular wave number as

k = 2p /?

or

? = 2p / 0.020p

=1.0*102cm

c)

the frequency is

f = ?/2p

= 4p/2p

= 2.0 Hz

d)

the wave speed is

v = f?

= (100cm)(2.0Hz)

= 2.0*102cm/s

e)

since the trignometric function is (kx -?t) , sothe wave propagates in th -x direction

f)

the maximum transverse speed is

umax =2pfym

= 2p(2.0Hz)(6.0cm)

= 75cm/s

g)

we have

y(3.5cm ,0.26s) = 6.0cmsin[0.020p(3.5) +4.0p(0.26)]

= -2.0cm

6 0
3 years ago
Starting from rest, a basketball rolls from the top to the bottom of a hill, reaching a translational speed of 6.1 m/s. Ignore f
tatiyna

Answer:

a) h=3.16 m, b)  v_{cm }^ = 6.43 m / s

Explanation:

a) For this exercise we can use the conservation of mechanical energy

Starting point. Highest on the hill

           Em₀ = U = mg h

final point. Lowest point

           Em_{f} = K

Scientific energy has two parts, one of translation of center of mass (center of the sphere) and one of stationery, the sphere

           K = ½ m v_{cm }^{2} + ½ I_{cm} w²

angular and linear speed are related

           v = w r

           w = v / r

            K = ½ m v_{cm }^{2} + ½ I_{cm} v_{cm }^{2} / r²

            Em_{f} = ½ v_{cm }^{2} (m + I_{cm} / r2)

as there are no friction losses, mechanical energy is conserved

             Em₀ = Em_{f}

             mg h = ½ v_{cm }^{2} (m + I_{cm} / r²)         (1)

             h = ½ v_{cm }^{2} / g (1 + I_{cm} / mr²)

for the moment of inertia of a basketball we can approximate it to a spherical shell

             I_{cm} = ⅔ m r²

we substitute

            h = ½ v_{cm }^{2} / g (1 + ⅔ mr² / mr²)

            h = ½ v_{cm }^{2}/g    5/3

             h = 5/6 v_{cm }^{2} / g

           

let's calculate

           h = 5/6 6.1 2 / 9.8

           h = 3.16 m

b) this part of the exercise we solve the speed of equation 1

          v_{cm }^{2} = 2m gh / (1 + I_{cm} / r²)

in this case the object is a frozen juice container, which we can simulate a solid cylinder with moment of inertia

              I_{cm} = ½ m r²

we substitute

             v_{cm } = √ [2gh / (1 + ½)]

             v_{cm } = √(4/3 gh)

let's calculate

             v_{cm } = √ (4/3 9.8 3.16)

             v_{cm }^ = 6.43 m / s

4 0
3 years ago
Could You Take 2 Elements From The Periodic Table Of Elements, and possibly make one of other 116 elements that are on the table
LekaFEV [45]
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There are 92 elements on the Periodic Table that are found in nature,
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