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jalayshiamartin
13.02.2021 •
Physics
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MU Unit 06 Momentum L Exam
A child is on a sled moving down a hill at 10 m/s. The combined mass of the sled and child is 100 kilograms. The momentum of the child and sled is
20 kg-m/s
2000 kg-m/s
1000 kg-m/s
5 kg•m's
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Ответ:
a) the modulus of elasticity (E) is 68.22 GPa
b) the modulus of elasticity in shear is 25.28 GPa
Explanation:
Given the data in the question;
First we determine the cross-sectional area A of the road;
A = π/4 × d²
given that; diameter d = 20 mm
we substitute
A = π/4 × ( 20 mm )²
A = π/4 × 400 mm
A = 314.159 mm²
Next, we find, the normal stress of the rod σ
σ = P / A
given that load p = 50 kN = 50,000 Newton
we substitute
σ = 50,000 N / 314.159 mm²
σ = 159.155 N/mm²
σ = 159.155 Mpa
Next, is the normal strain ε
ε = δ / L
given that; change in length δ = 1.40 mm and Length of rod L = 600 mm
we substitute
ε = 1.40 mm / 600 mm
ε = 0.002333
Now, we find the modulus of elasticity;
we know that;
σ = Eε
modulus of elasticity E = σ / ε
we substitute
E = 159.155 Mpa / 0.002333
E = 68219.031 MPa
E = ( 68219.031 / 1000 ) GPa
E = 68.22 GPa
Therefore, the modulus of elasticity (E) is 68.22 GPa
b)
we know that the Poisson's ratio v is;
v = -(ε
/ ε )
v = - (((d
- d)/d) / ε )
where d
is the final diameter of the rod ( 19.9837 mm ) and ε
is the lateral strain
so we substitute
v = - ((( 19.9837 - 20 ) / 20 ) / 0.002333 )
v = - (( -0.0163 / 20 ) / 0.002333 )
v = - ( - 0.000815 / 0.002333 )
v = - ( - 0.3493 )
v = 0.3493
So, our shear modulus will be;
G = E / 2( 1 + v )
we substitute
G = 68.22 GPa / 2( 1 + 0.3493 )
G = 68.22 GPa / 2( 1.3493 )
G = 68.22 GPa / 2.6986
G = 25.28 GPa
Therefore, the modulus of elasticity in shear is 25.28 GPa