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Neko
3 months ago
10

A specimen of steel has a rectangular cross section 20 mm wide and 40 mm thick, an elastic modulus of 207 GPa, and a Poisson’s r

atio of 0.30. If this specimen is pulled in tension with a force of 60,000 N, what is the change in width if deformation is totally elastic?
Physics
1 answer:
Softa [3K]3 months ago
6 0

Response: The width decreases by 2.18 × 10^(-6) m

Clarification:

Given data;

Shear Modulus; E = 207 GPa = 207 × 10^(9) N/m²

Force; F = 60000 N.

Poisson’s ratio; υ = 0.30

The initial width is 20 mm, and the thickness is 40 mm.

Area = 20 × 10^(-3) × 40 × 10^(-3)

Area = 8 × 10^(-4) m²

The formula for shear modulus is;

E = σ/ε_z

where σ represents stress calculated as Force(F)/Area(A)

while ε_z stands for longitudinal strain.

Thus;

E = (F/A)/ε_z

ε_z = (F/A)/E

ε_z = (60,000/(8 × 10^(-4)))/(207 × 10^(9))

ε_z = 3.62 × 10^(-4)

Next, the lateral strain is given by;

ε_x = - υ × ε_z

ε_x = -0.3 × 3.62 × 10^(-4)

ε_x = -1.09 × 10^(-4)

The change in width can be determined as;

Δw = w_o × ε_x

Where w_o denotes the original width = 20 × 10^(-3) m

So; Δw = 20 × 10^(-3) × -1.09 × 10^(-4)

Δw = -2.18 × 10^(-6) m

A negative sign indicates a reduction in width.

Therefore, the width decreases by 2.18 × 10^(-6) m

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Answer:

Statements 4, 6 & 7 are incorrect.

Explanation:

In any elastic collision, the overall momentum vector sum of the system remains zero.

In this scenario, an elastic collision occurs between the ball and a stationary wall. The ball's velocity will consistently revert after the impact, leading to a change in direction of momentum.

The initial momentum of the ball is represented as:

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m = mass of the ball

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post-collision for the elastic interaction:

p=m.(-v)

  • Here, the momentum changes solely in direction, thus contradicting statement 7.
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3 months ago
A rope connects boat A to boat B. Boat A starts from rest and accelerates to a speed of 9.5 m/s in a time t = 47 s. The mass of
ValentinkaMS [3465]

Answer: 339.148N

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Given data:

Time (t) = 47s

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Since both boats are linked, movement of A causes B to move as well.

What is the acceleration of boat A?

Applying the motion formula:

V = u + at

9.5 = 0 + a * 47

a = 9.5 / 47

a = 0.2021 m/s²

To determine the force necessary to accelerate boat B, as both boats experience the same force:

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Given that there is a frictional force of 230N acting on boat B, the overall force (Tension) becomes:

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A person who climbs up something (e.g., a hill, a ladder, the stairs) from the ground gains potential energy. a person's weight
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The following values have been provided:

weight w = 240 lb = 1,067.52 N

energy E = 3,000 J

 

The equation for potential energy is:

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where h indicates the height that the person needs to ascend, therefore:

h = 3000 / 1067.52

h = 2.81 m

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<span>
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<span>Thus, he must ascend 2.81 meters</span>

3 0
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