spotlight on a boat is 2.5 m above the water, and the light strikes the water at a point that is 8.0 m horizontally displaced fr
1 answer:
Answer:
Explanation:
Let i be the angle of incidence and r be the angle of refraction .
From the figure
Tan ( 90 - i ) = 2.5 / 8
cot i = 2.5 / 8
Tan i = 8 / 2.5 = 3.2
i = 72.65°
From snell's law
sini / sin r = refractive index
sin 72.65 / sinr = 1.333
sin r = .9545 / 1.333
= .72
r = 46⁰
From the figure
Tan r = d / 4
Tan 46 = d /4
d = 4 x Tan 46
= 4 x 1.0355
=4.14 m .
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Answer:
The true stress at true strain 0.05cm/cm is 80MPa
Explanation:
Given that
the strength coefficient is K
true strain is ε
strain hardening exponent is n
initial diameter of bar is d = 1cm, (10mm)
tensile force is F
engineering stress(S) = 120
the engineering stress(S) =
To find force (F) =
120 =
F = 120 * (π/4) * (100)
F = 9425N
Calculate the true strain (ε) = In (l₀ / l₁)
where
l₀ = initial length of the metallic bar = 3cm
l₁ = final length of metallic bar = 3.5cm
ε = In (3.5 / 3)
= In 1.1667
= 0.154cm/cm
Calculate the true stress (σ) at fracture point
=
tensile force is F and final diameter of bar is d₁ (d in the eqn)
Substitute 9425 N for F and 0.926 cm (9.26mm) for d₁ (d in the eqn)
σ =
= 140MPa
To find the strength coefficient (K) of the material bar
K =
K =
= 356.75MPa
To calculate the true stress σ true strain of 0.05cm/cm
K = 356.75MPa
σ =
=
= 80MPa
The true stress at true strain 0.05cm/cm is 80MPa
Answer:
B. -900 kg-m/s2
Explanation:
First of all, we need to calculate the acceleration of the hockey player, which is given by:
where
v = 12 m/s is the final speed
u = 18 m/s is the initial speed
t = 0.6 s is the time
Substituting into the formula, we find
And now we can calculate the force exerted by using Newton's second law:
where m=90 kg is the mass of the hockey player. Substituting into the formula, we find