1. A particle of mass M is acted upon by a force that has a initial
magnitude F0 when t=0 and decrease at a uniform rate
until when t=t1, its magnitude is zero. It is moving
across the X-axis. Find the velocity and coordinate of the
particle when t=t2 assuming that t2 >
t1. Assume xt=0=0 and
(dx/dt)t=0=0
Ans:
Velocity=F0t1/2M
Displacement=(F0t1/2M)(t2-t1/3)
2. A wheel of radius r rolls without slip along
the x-axis with constant speed v0. Find out the
motion(velocity and acceleration ) of the point A on the rim of
the wheel which starts from the origin O. Take Y axis as
perpendicular at X axis at origin
Ans:
dx/dt=v0[1-cos(v0t/r)]
dy/dt=v0sin(v0t/r)
d2x/dt2=(v02/r)sin(v0t/r)
d2y/dt2=(v02/r)cos(v0t/r)
3. A body moves under the action of a constant force F through fluid that opposes the motion with a force proportional to the square of the velocity that is Ax2. Show that the limiting velocity is VL=(F/A)1/2.
4. A Bungee Jumper is attached to one end of a long elastic rope. The other end of the elastic rope is fixed to a high bridge. The Jumper steps off the bridge and falls from rest towards the river below. He does not hit the river below. The mass of the jumper is M and length of un-stretched rope is L. Force constant of the rope is K and gravitational field strength is g. Mass of rope is negligible, air resistance is negligible.
1. Find out the distance y dropped by the jumper before coming instantaneously to rest for the first time
2. Maximum speed attained by the jumper during this drop
3. The time taken during the drop before coming
to rest for the first time
Ans:
y=[KL+mg+√(2mgKL+m2g2)]/k
v=√(2gL+mg2/k)
t=√(2L/g) +
√(m/k)tan-1{-√(2KL/mg)}
Source: http://physicsgoeasy.blogspot.com/
Image Credit : roland
