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ch4aika [34]
2 years ago
12

The distance between an object and its image formed by a diverging lens is 5.80 cm. The focal length of the lens is -2.60 cm. Fi

nd (a)the image distance and (b) the object distance.
Physics
1 answer:
pentagon [3]2 years ago
7 0

Answer:

a) 1.55 cm

b) 4.25 cm

Explanation:

Given:

Distance between an object and the image = 5.80 cm

Focal length of the lens, f = -2.60 cm

let the image distance be 'v' and the object distance be 'u'

thus,

u + v = 5.80 cm

or

u = 5.80 - v

from the lens formula, we have

\frac{1}{f}=\frac{1}{u}+\frac{1}{v}

on substituting the values, we have

\frac{1}{-2.60}=\frac{1}{5.80-v}+\frac{1}{v}

on rearranging, we get

-3.84 × (v × (5.80 - v)) = v + 5.80 - v

or

-2.23v + 3.84v² = 5.80

or

3.84v² - 2.23v - 5.80 = 0

on solving the quadratic equation, we get

v = 1.55 cm

and u = 5.80 - 1.55 = 4.25 cm

hence,

a) 1.55 cm

b) 4.25 cm

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Answer:

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Explanation:

(a) To calculate the initial speed of the bullet, you first take into account that the kinetic energy of both wood block and bullet, just after the bullet impacts the block, is equal to the potential gravitational energy of block and bullet when the cord is at 60° respect to the vertical.

The potential energy is given by:

U=(M+m)gh       (1)

U: potential energy

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m: mass of the bullet = 6g = 6.0*10^-3 kg

g: gravitational constant = 9.8m/s^2

h: distance to the ground

The distance to the ground is calculate d by using the information about the length of the cord and the degrees of the cord respect to the vertical:

h=l-lsin\theta\\\\h=2.2m-2,2m\ sin60\°=0.29m

The potential energy is:

U=(1kg+6*10^{-3}kg)(9.8m/s^2)(0.29m)=2.85J

Next, the potential energy is equal to kinetic energy of the block and the bullet at the beginning of its motion:

U=\frac{1}{2}(M+m)v^2\\\\v=\sqrt{2\frac{U}{M+m}}=\sqrt{2\frac{2.85J}{1kg+6*10^{-3}kg}}=2.38\frac{m}{s}

Next, you use the momentum conservation law, in order to calculate the speed of the bullet before the impact:

Mv_1+mv_2=(M+m)v    (2)

v1: initial velocity of the wood block = 0m/s

v2: initial speed of the bullet

v: speed of bullet and block = 2.38m/s

You solve the equation (2) for v2:

M(0)+mv_2=(M+m)v    

v_2=\frac{M+m}{m}v=\frac{1kg+6*10^{-3}kg}{6*10^{-3}kg}(2.38m/s)\\\\v_2=399.04\frac{m}{s}

The speed of the bullet before the impact with the wood block is 399.04 m/s

(b) The impulse is gibe by the change in the velocity of the block, multiplied by the mass of the block:

I=M\Delta v=M(v-v_1)=(1kg)(2.38m/s-0m/s)=2.38kg\frac{m}{s}

The impulse is 2.38 kgm/s

(c) The force on the cord after the impact is equal to the centripetal force over the block and bullet. That is:

T=F_c=(M+m)\frac{v^2}{l}=(1.006kg)\frac{(2.38m/s)^2}{2.2m}=2.59N    

The force on the cord after the impact is 2.59N

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u = Initial velocity

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From equation of motion we have

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A stretched rubber band is storing <em>elastic potential energy. (A)</em>

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