Question

a very light ideal spring having a spring constant of 8.2 N/cm is used to lift a 2.2 kg tool with an upward acceleration of 3.25 m/s^2. if the spring has negligible length when it is not stretched, how long is it while it is pulling the tool upward?

Answer 1

Answer on Question #57022, Physics / Mechanics | Relativity

A very light ideal spring having a spring constant of $8.2 \, \text{N/cm}$ is used to lift a $2.2 \, \text{kg}$ tool with an upward acceleration of $3.25 \, \text{m/s}^2$ . If the spring has negligible length when it is not stretched, how long is it while it is pulling the tool upward?

Solution:

Sum of the vertical forces (up is positive) = mass * acceleration

What are the vertical forces? Weight, which acts down (negative) and the force, which acts up (positive).

$$m a = F _ {s p r i n g} - m g$$ $$F _ {s p r i n g} = m (a + g)$$

Then use Hooke's Law

$$F _ {s p r i n g} = k x$$ $$k x = m (a + g)$$ $$x = \frac {m (a + g)}{k} = \frac {(2 . 2 \mathrm {k g}) (3 . 2 5 + 9 . 8 1 \mathrm {m / s ^ {2}})}{(8 . 2 \mathrm {N / c m})} = 3. 5 0 \mathrm {c m}$$

Answer: $3.50\mathrm{cm}$

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