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soldi70 [24.7K]
3 years ago
11

Particle A has half the mass and eight times the kinetic energy of particle B. What is the speed ratio vA / vB?

Physics
1 answer:
Marta_Voda [28]3 years ago
8 0

Answer:

Use the equation "KE=½mv²", and use some algebra. > "Particle A has two times the mass...of particle B" mA = 2mB > "Particle A has...8 situations the kinetic power of particle B" KE_A = 8(KE_B) or: ½(mA)(vA)² = 8(½(mB)(vB)²) the rest is uncomplicated algebra: in basic terms sparkling up the above equation for "vA/vB". (hint: start up by utilising dividing the two factors by utilising "(mB)(vB)²". Then make the substitution: mA/mB = 2 (from the 1st eq0.5 ma *  VA^2 = 8 * 0.5 * mb * VB^2

0.5 * 0.5*mb *  VA^2 = 8 * 0.5 * mb * VB^2

0.5 * 0.5*  VA^2 = 8 * 0.5 * VB^2

VA/VB = 4uation))

Explanation:

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Answer:

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As per the question:

Length, a = 4 km

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In order to minimize the cost let us denote the side of the square bottom be 'a'

Thus the area of the bottom of the square, A = a^{2}

Let the height of the bin be 'h'

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C = 2sh

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Total cost, C_{t} = 2a^{2} + 2ah            (2)

From eqn (1):

h = \frac{128}{a^{2}}

Using the above value in eqn (1):

C(a) = 2a^{2} + 2a\frac{128}{a^{2}} = 2a^{2} + \frac{256}{a}

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Differentiating the above eqn w.r.t 'a':

C'(a) = 4a - \frac{256}{a^{2}} = \frac{4a^{3} - 256}{a^{2}}

For the required solution equating the above eqn to zero:

\frac{4a^{3} - 256}{a^{2}} = 0

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Also

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