P. 3797. On a horizontal frictionless table a stick of mass M, length of L and of homogeneous mass distribution is standing.
a) With what velocity had a small body of mass m slid into it, if the stick hit the table after a turn of an angle ?
b) How far was the mass center of the stick from the small body at this moment?
(The collision of the small body and the stick is perfectly elastic.) (Data: M=0.6 kg, m=0.2 kg, L=0.8 m, =60o.)
P. 3798. A 0.8 m long rod joins to a vertical axle with a bearing at its middle. The rod has negligible mass and it is frictionless. We thread point-like pierced balls of masses of 200 g on both of its ends. The two balls positioned symmetrically on both sides of the axis are linked with a thin thread of a length of 0.2 m. At the ends of the rod there are non-elastic bumpers. We spin this system with an angular velocity of 2 s-1 and then we burn the thread.
a) What path do the balls follow?
b) How much does the rod turn in 1 s after burning the fibre.
c) In what time does the rod turn by an angle of 180o?
d) What distance is done by the balls during the half turn of the rod?
e) What percentage is the mechanical loss?
P. 3800. A metal ring having three metallic spokes of lengths r=0.2 m is in a vertical plane and can spin around a fixed horizontal axis in a homogeneous magnetic field of a magnetic induction of B=0.5 T. The lines of magnetic field are perpendicular to the plane of the metal ring. Between the axis of the metal ring and its perimeter we connect a consumer of a resistance of 0.15 with the help of two sliding contacts. We fix a thread of negligible mass to the rim of the ring and wind it several times around the ring and to its end we fix a body of a mass of 20 g. At a given moment we release the body of mass m. The friction is negligible everywhere, the resistance of the ring, the spokes and the connected wiring is also negligible.
a) What is the torque exerted on the ring with the spokes by the magnetic forces when the body of mass m is moving with a constant velocity?
b) What current is flowing through the consumer when the velocity of the body of mass m is 3 m/s?
c) What is the highest velocity of the body of mass m?