Respuesta :
Answer:
[tex]F = 4.16 N[/tex]
Explanation:
Let the coefficient of restitution is "e"
so we have
[tex]e = \frac{v_2 - v_1}{u_1 - u_2}[/tex]
here we have
[tex]v_2 - v_1 = eu[/tex]
now we have by momentum conservation
[tex]mu = mv_1 + mv_2[/tex]
[tex]v_1 + v_2 = u[/tex]
now we have
[tex]v_2 = \frac{u}{2}(1 + e)[/tex]
[tex]v_1 = \frac{u}{2}(1 - e)[/tex]
now we have the ratio of final kinetic energy and initial kinetic energy given as 0.86
so we have
[tex]0.86 = \frac{0.5mv_1^2 + 0.5mv_2^2}{0.5 mu^2}[/tex]
[tex]0.86 u^2 = v_1^2 + v_2^2[/tex]
[tex]0.86 u^2 = \frac{u^2}{4}(1 + e)^2 + \frac{u^2}{4}(1 - e)^2[/tex]
[tex]3.44 = 2 + 2e^2[/tex]
[tex]e = 0.85[/tex]
so we have
[tex]v_1 = \frac{u}{2}(1 - 0.85) = 0.076u[/tex]
now change in velocity of first ball is given as
[tex]\Delta v = u - 0.076 u[/tex]
[tex]\Delta v = 0.924u[/tex]
now acceleration of the ball is given as
[tex]a = \frac{\Delta v}{\Delta t}[/tex]
[tex]a = \frac{0.924\times 0.45}{0.01}[/tex]
[tex]a = 41.6 m/s^2[/tex]
so the force on the ball during collision is
[tex]F = ma[/tex]
[tex]F = 0.1 \times 41.6[/tex]
[tex]F = 4.16 N[/tex]
