Question

You place a large pebble in a slingshot, pull the elastic band back to your chin, and release it, launching the pebble horizontally at a speed of 100 cm/s. You then repeat the exact same procedure (pulling the elastic band back the same distance) with a smaller pebble. The smaller pebble leaves the slingshot with a speed of 500cm/s. How does the mass of the larger pebble compare to that of the smaller pebble? Select the correct answer O The larger pebble has v5 times more mass O This question cannot be answered without knowing the effective spring constant of the elastic band. O The larger pebble has 2 times more mass. The larger pebble has 5 times more mass. Your Answer O The larger pebble has 25 times more mass.

Answer 1

Answer:

The larger pebble has 25 times more mass.

Explanation:

To solve the exercise it is necessary to apply the work and energy conservation equations.

For the case described, the work done must be preserved and must be the same, that is,

$W = 0$

By definition work linked to the conservation of kinetic energy would be given by

$\Delta KE = W = 0$

$\Delta KE = 0$

$KE_{larger}-KE_{smaller} = 0$

$KE_{larger}=KE_{smaller}$

$\frac{1}{2}m_lv_l^2 = \frac{1}{2}m_sv_s^2$

$m_lv_l^2 = m_sv_s^2$

The ratio between the mass and the velocity would be,

$\frac{m_l}{m_s}=\frac{v_s^2}{v_l^2}$

$\frac{m_l}{m_s} = \frac{500^2}{100^2}$

$\frac{m_l}{m_s} = 25$

Therefore the answer is: The larger pebble has 25 times more mass.