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ch4aika [34]
3 years ago
5

A metal wire breaks when its tension reaches 100 newton. If the radius and length of the wire were both doubled then it would br

eak when the tension reached how many newtons
Physics
1 answer:
serg [7]3 years ago
7 0

Answer:

200 N

Explanation:

Since Young's modulus for the metal, E = σ/ε where σ = stress = F/A where F = force on metal and A = cross-sectional area, and ε = strain = e/L where e = extension of metal = change in length and L = length of metal wire.

So,  E = σ/ε = FL/eA

Now, since at break extension = e.

So making e subject of the formula, we have

e = FL/EA = FL/Eπr² where r = radius of metal wire

Now, when the radius and length are doubled, we have our extension as e' = F'L'/Eπr'² where F' = new force on metal wire, L' = new length = 2L and r' = new radius = 2r

So, e' = F'(2L)/Eπ(2r)²

e' = 2F'L/4Eπr²

e' = F'L/2Eπr²

Since at breakage, both extensions are the same, e = e'

So,  FL/Eπr² = F'L/2Eπr²

F = F'/2

F' = 2F

Since F = 100 N,

F' = 2 × 100 N = 200 N

So, If the radius and length of the wire were both doubled then it would break when the tension reached 200 Newtons.

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Ans: R = Ball Travelled = 92.15 meters.

Explanation:
First we need to derive that formula for the "range" in order to know how far the ball traveled before hitting the ground.

Along x-axis, equation would be:
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x = x_o + v_o_xt

Since v_o_x = v_ocos \alpha and x_o=0; therefore above equation becomes,

x = v_ocos \alpha t --- (A)

Now we need to find "t", and the time is not given. In order to do so, we shall use the y-direction motion equation. Before hitting the ground y ≈ 0 and a = -g; therefore,

=> y = y_o + v_o_yt -  \frac{gt^2}{2}
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Since v_o_y = sin \alpha; therefore above equation becomes,
t = \frac{2v_osin \alpha }{g}

Put the value of t in equation (A):

(A) => x = v_ocos \alpha \frac{2v_osin \alpha }{g}

Where x = Range = R, and 2sin \alpha cos \alpha = sin(2 \alpha ); therefore above equation becomes:

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Now, as:
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and \alpha = 35°
and g = 9.8 m/(s^2)

Hence,
R = (31)^2 *\frac{sin(2 *35 )}{9.8}

Ans: R = 92.15 meters.

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