- #1
zhenyazh
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Hi,
i am preparing for the test and have a problem with the following question.
an image is attached
A thin stick of mass M = 4.9 kg and length L = 2.6 m is hinged at the top. A piece of clay, mass m = 1.0 kg and velocity V = 4.9 m/s hits the stick a distance x = 2.20 m from the hinge and sticks to it. What is the angular velocity of the stick immediately after the collision?
this i found 6.79×10-1 rad/s
What is the ratio of the final mechanical energy to the initial mechanical energy?
if i understand correctly, the final mechanical energy is before the bar starts to move up.
so i should take into consideration only the kinetic energy.
the initial energy is of course the energy of the clay which i regard as a point body
and thus 0.5mv^2.
the final energy is the energy of bar and clay joined.
this is 0.5Iw^2+0.5mu^2 where u is the velocity of the center of mass of the joint body.
if i know that angular speed of the joint body i can use w=ur, where r is the distance
between the centre of mass and the point with respect to which i am doing my calculations. that would be the distance from the pivot that holds the bar.
Xcm=(mx+lM)/(m+M)=2.532
that gives me
0.5Iw^2+0.5mw^2*2.532^2.
but i get the wrong answer.
where am i wrong?
thanks
i am preparing for the test and have a problem with the following question.
an image is attached
A thin stick of mass M = 4.9 kg and length L = 2.6 m is hinged at the top. A piece of clay, mass m = 1.0 kg and velocity V = 4.9 m/s hits the stick a distance x = 2.20 m from the hinge and sticks to it. What is the angular velocity of the stick immediately after the collision?
this i found 6.79×10-1 rad/s
What is the ratio of the final mechanical energy to the initial mechanical energy?
if i understand correctly, the final mechanical energy is before the bar starts to move up.
so i should take into consideration only the kinetic energy.
the initial energy is of course the energy of the clay which i regard as a point body
and thus 0.5mv^2.
the final energy is the energy of bar and clay joined.
this is 0.5Iw^2+0.5mu^2 where u is the velocity of the center of mass of the joint body.
if i know that angular speed of the joint body i can use w=ur, where r is the distance
between the centre of mass and the point with respect to which i am doing my calculations. that would be the distance from the pivot that holds the bar.
Xcm=(mx+lM)/(m+M)=2.532
that gives me
0.5Iw^2+0.5mw^2*2.532^2.
but i get the wrong answer.
where am i wrong?
thanks