A mass m is pushed against the end of a spring, compressing it by an amount d fr
ID: 2237987 • Letter: A
Question
A mass m is pushed against the end of a spring, compressing it by an amount d from its relaxed position. The spring has spring constant k. The mass is released from rest and slides along a flat frictionless surface. It then slides into a frictionless semicircle of radius R.
(a) Find an expression for the speed of the mass as a function of ?, m, d, k, R, and g.
(b) What is the largest angle the mass reaches before it stops?
(c) What is the normal force when the mass reaches its largest angle obtained in part (b)?
Explanation / Answer
a)applying conservation of energy 1/2*k*d^2=1/2*m*v^2+m*g*h h=Rcos? v=sqrt(k*d^2-2*mgRcos?/(m)) ans b)largest angle is when whole potential energy of spring is converted into potential energy due to gravity 1/2*k*d^2=m*g*R*cos? ?=arccos(1/2*k*d^2/m*g*R) c) Normal force N=mgsin?=mg*sqrt(1-(1/2*k*d^2/m*g*R)^2 ) ans
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.