Question

A block of mass 3 kg compresses a horizontal spring by 0.4 m. When it is released the block moves across a horizontal plain a distance of 2.4 m before coming to rest. If the coefficient of friction between the block and the table is 0.3, what is the force constant?

Answer 1

Answer on Question#68280-Physics / Other

A block of mass $m = 3$ kg compresses a horizontal spring by $x = 0.4$ m. When it is released the block moves across a horizontal plain a distance of $s = 2.4$ m before coming to rest. If the coefficient of friction between the block and the table is $\mu = 0.3$, what is the force constant?

Solution

The change of energy is equal to work done

$$\frac{k x^{2}}{2} = \mu m g s.$$

So

$$k = \frac{2 \mu m g s}{x^{2}},$$ $$k = \frac{2 \times 0.3 \times 3 \times 9.8 \times 2.4}{0.4^{2}} = 264.6 \ \frac{\mathrm{N}}{\mathrm{m}}.$$

Answer $= 264.6 \ \frac{\mathrm{N}}{\mathrm{m}}$.

Answer provided by https://www.AssignmentExpert.com