1. Consider an elastic collision with three billiard balls which equal mass. The
ID: 1781620 • Letter: 1
Question
1. Consider an elastic collision with three billiard balls which equal mass. The balls initially are separated by an equal distance d. The balls are on a straight line. The first ball has a velocity of 1 The other two balls are initially at rest What will be the velocity of the third ball after the second ball collide with the third one. The second ball start moving after the collision between the first and the second one. 2. A student sitting on a stool that can rotate freely. The student holds a bicycle wheel rotating around the verical axes. The moment of inertia of the student is Istadent and the moment of inertia of the bicycle wheel is Ineyde The angular velocity of the bicycle wheel is wuhed = 10 and the angular velocity of the student sitting on the stool is wstudent = 0.1 The students turns the wheel at 90 degrees (the wheel is rotating after the turn in the perpendicular direction such that the angular velocities Wheel and are perpendicular to each other. a) Assuming that the stool only can rotate around the vertical axes ,find the angular velocity of the student after he turns the wheel at 90 degrees. 3. The equilibrium condition for a body. a) Write the conditions for static equilibrium for a ladder which makes an angle of 30 degrees with the wall . The mass of the ladder is M and the length is L b) Determine the force from the wall on the ladder in units of Mg. key idas Conservation of linear momentum: Conservation of Energy Angular momentum of abody is Iw. I is the moment of inertia and w is the angular Torque is defined as:= × F velocityExplanation / Answer
1.
For elastic collision between first and second mass we use eqns,
v2f=[(2m1)/(m1+m2)v1i – [(m1-m2)/(m1+m2)]v2i
v2f=[(m1-m2)/(m1+m2)v1i + [(2m2)/(m1+m2)]v2i
Since m1=m2=m and v2i=0
We get
v1f= 0m/s and v2f = v1i = 1.0m/s
For elastic collision between first and second mass we use eqns,
V3f=[(2m2)/(m2+m3)v2i – [(m2-m3)/(m2+m3)]v3i
V3f=[(m2-m3)/(m2+m3)v2i + [(2m3)/(m2+m3)]v3i
Since m2=m3=m and v3i=0
We get
v3f= 0m/s and v3f = v2i = 1.0m/s
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