Question

If a small mass starts off with a velocity (v_0) and runs into another mass (M) that's at rest, and they then stick together, what is direction will they be moving in? How does the magnitude of V_final compare to v_0? If I have a pendulum 1 meter long with a 5 kg mass at the bottom, and swing it so that its maximum speed is 3 m/s, what is the maximum height the bottom of the pendulum will reach? Geometry practice: Write a mathematical expression for h in terms of theta & L for a pendulum.

Answer 1

3)

let,

small mass is m

by using conservation of momentum,

m*v0+M*(0)=(m+M)*vf

==> vf=(m/(m+M))*v0

here,

two masses stick to gethere and they travel in the direction of the velocity of vo

4)

length of the pendulum is l=1m

mass m=5kg

maximum speed Vo=3m/sec

===> 1/2*m*v0^2=m*g*h

1/2*vo^2=g*h

1/2*3^2=9.8*h

====> h=0.46 m

maximum height, h=0.46 m

5)

here,

1/2*m*v^2-1/2*m*u^2=m*g*h

1/2*m*v^2-1/2*m*u^2=m*g*l*(1-cos(thet))

v^2-u^2=2*g*l*(1-cos(thet))

here,

h=l-l*cos(theta)

h=l(1-cos(theta))