1.

A particle of mass m strikes a smooth floor with speed u at angle of incidence theta with the normal. The coefficient of resultant is e. Find the magnitude and direction of velocity with which the particle rebounds. Also, find the impulse and loss in K.E.

Answer» <html><body><p></p>Solution :Before the collision: <br/> After the collision: <br/> Since there is no force <a href="https://interviewquestions.tuteehub.com/tag/along-1974109" style="font-weight:bold;" target="_blank" title="Click to know more about ALONG">ALONG</a> the surface , hence the velocity component remains same. <br/> `<a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a> sin alpha = u sin theta`(i) <br/> Due to the normal force between the particle and the floor , the velocity component becomes `e <a href="https://interviewquestions.tuteehub.com/tag/times-1420471" style="font-weight:bold;" target="_blank" title="Click to know more about TIMES">TIMES</a>` in opposite direction <br/> `v cos alpha = e u cos theta`(<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) <br/> `v = sqrt((v sin alpha)^(2) + (v cos alpha)^(2)) = u sqrt(sin^(2) theta + e^(2) cos^(2) theta)` <br/> `tan alpha = ( v sin alpha)/(v cos alpha) = (1)/(e) tan theta` <br/> If the collision is elastic , `e = 1 , v = u , alpha = theta` <br/> `J_(x) = 0` <br/> `J_(y) = m(v cos alpha + u cos theta)` <br/> `= m ( e u cos theta + u cos theta) = mu cos theta ( 1 + e)` <br/> `J = mu cos theta ( 1 + e)` <br/> `Delta <a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a> = (1)/(2) mu^(2) - (1)/(2) m u^(2)= (1)/(2) mu^(2) cos^(2) theta ( 1 - e^(2))` <br/> `Delta` K: loss in `K.E.` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CPS_V01_C10_S01_069_S01.png" width="80%"/><br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CPS_V01_C10_S01_069_S02.png" width="80%"/></body></html>


Discussion

No Comment Found

Related InterviewSolutions