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blsea [12.9K]
3 years ago
10

When a 70 kg man sits on the stool, by what percent does the length of the legs decrease? Assume, for simplicity, that the stool

's legs are vertical and that each bears the same load.
Physics
1 answer:
allochka39001 [22]3 years ago
7 0

The diameter of one leg of the stool is missing and it's 2cm.

Answer:

(ΔL/L) = 0.00729%

Explanation:

If the Weight of the man is W, the weight will be distributed equally on the 3 legs and so the reactions for each leg will be W/3 or F/3.

Now, Youngs modulus(Y) of douglas fir wood is about 1.3 x 10^(10) N/m^2. Gotten from youngs modulus of common materials.

Now, weight of man is 70kg.

Now diameter of one leg is 2cm.so radius of one leg = 2/2 = 1cm = 1 x 10^(-2)m

Area for one leg is; π( 1 x 10^(-2)m)^2 = 3.14 x 10^(-4)m

Now as stated earlier, the force on one leg is; F/3.

Now F = mg = 70 x 9.81 = 686.7N

So, force on one leg = 686.7/3 = 228. 9N

Now we know youngs modulus(Y) = Stress/Strain.

Stress = F/A while Strain = ΔL/L

Therefore Y = (F/A) / (ΔL/L)

And therefore, (ΔL/L) = F/(AY)

So (ΔL/L) = 228.9/(3.14 x 10^(-4))x(1.3 x 10^(10)) = 7. 29 x 10^(-5)

When expressed in percentage, it becomes 0.00729%

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Answer:

The kinetic coefficient of friction of the crate is 0.235.

Explanation:

As a first step, we need to construct a free body diagram for the crate, which is included below as attachment. Let supposed that forces exerted on the crate by both workers are in the positive direction. According to the Newton's First Law, a body is unable to change its state of motion when it is at rest or moves uniformly (at constant velocity). In consequence, magnitud of friction force must be equal to the sum of the two external forces. The equations of equilibrium of the crate are:

\Sigma F_{x} = P+T-\mu_{k}\cdot N = 0 (Ec. 1)

\Sigma F_{y} = N - W = 0 (Ec. 2)

Where:

P - Pushing force, measured in newtons.

T - Tension, measured in newtons.

\mu_{k} - Coefficient of kinetic friction, dimensionless.

N - Normal force, measured in newtons.

W - Weight of the crate, measured in newtons.

The system of equations is now reduced by algebraic means:

P+T -\mu_{k}\cdot W = 0

And we finally clear the coefficient of kinetic friction and apply the definition of weight:

\mu_{k} =\frac{P+T}{m\cdot g}

If we know that P = 400\,N, T = 290\,N, m = 300\,kg and g = 9.807\,\frac{m}{s^{2}}, then:

\mu_{k} = \frac{400\,N+290\,N}{(300\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}

\mu_{k} = 0.235

The kinetic coefficient of friction of the crate is 0.235.

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The law of conservation of energy states that in absence of frictional forces, the mechanical energy of an object (given by the sum of its kinetic and potential energy) is conserved. In such a situation, the skateboarder would never stop his motion, because potential energy is continuously converted into kinetic energy and vice-versa, but the total energy remains the same so he would never stop.

In a real world, however, this is not true. In fact, in a real world some frictional force are present, in particular:

- friction: this force is due to the contact between the skateboard and the surface of the halfpipe, and its direction is always opposite to the motion of the skateboarder

- Air resistance: this force is due to the resistance opposed by the molecules of air that the skateboarder meets during his motion, and its direction is also opposite to the motion of the skateboarder

This two forces are said to be non-conservative forces, which means that they cause some of the mechanical energy of the skateboarder to be "lost", in the sense that it is dissipated as heat and it is no longer available for the skateboarder.

Therefore, the correct option is

Friction and air resistance cause some of his kinetic energy to be “lost”. This makes him slow down.

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Answer:

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