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3 years ago

What is the maximum height a 95 W motor may vertically lift a 120 N weight in 6.2 s?

Physics

1 answer:

leva [86]3 years ago

4 0

Answer:

a. 4.9 m

Explanation:

To solve this problem we must take into account that power is defined as the relationship between the work and the time in which the work is done.

P = W/t

where:

P = power = 95 [W] (units of watts)

W = work [J] (units of Joules)

t = time = 6.2 [s]

We can clear the work from the previous equation.

W = P*t

W = 95*6.2 = 589 [J]

Now we know that the work is defined by the product of the force by the distance, therefore we can express the work done with the following equation.

W = F*d

where:

F = force = 120 [N] (units of Newtons)

d = distance [m]

d = W/F

d = 589/120

d = 4.9 [m]

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Explanation:

1) Data Given

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We need to use Linear thermal expansion formula since the space created would be a change on 1 dimension, the increase of the temperature will increase the length of the steel. The formula is given by:

$\Delta L = L_i \alpha_{steel} \Delta T$

We have everything except the $\alpha_{steel}$ , so we look for this on a book and we find that $\alpha_{steel} = 1.2 x 10^{-5} C^{-1}$ , so we can replace.

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3) Calculate the stress of the steel

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$\sigma = \frac{F_n}{A}$

Since we don't have the force and the Area, we need to look for another way to find the stress.

For this we can use the concept called Young's Modulus, defined as : "the mechanical property that measures the stiffness of a solid material", and the formula for this is given by:

$Y =\frac{F L}{A \Delta L}$ (1)