Physics problems

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A student swings a stopper of mass 0.32 kg in a horizontal circle (parallel to the floor), as shown in the figure.

The string has a length L = 0.29 m, and is swung so that it remains at an angle of θ = 70° from the vertical.

A constant tension in the string is maintained as the stopper is swung in a circular path at this angle.

Determine the linear speed v (in m/s) necessary to keep the stopper revolving in this circular path.

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An object of mass 4g on a string is whirled with increasing speed in a horizontal circle, as shown above.
When the string breaks, the object has speed 9m/s and the circular path has radius 18cm and is a height 1.0m above the ground.

Neglect air resistance.
Determine the tension (in N) in the string as it breaks.

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Two identical objects of mass 1.6kg move on a one-dimensional, horizontal air track.

Object m2 initially moves to the right with speed v2=1.4m/s .

Object m1 initially moves to the right with speed 4.4×v2, so that it collides with object m2.

Friction is negligible.

When the experiment is performed, after the collision, object m1 moves to the right with a speed 3.0×v2.

Determine the kinetic energy dissipated in this experiment.

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A small and a large ball, of mass m1=0.39kg and m2=1.66kg respectively, are arranged as shown.

The balls are then simultaneously dropped from rest.

When the large ball strikes the floor, the balls have fallen a height H=0.48m. Assume air resistance is negligible.

Immediately after striking the floor, the large ball is moving upward with speed vb and collides head-on with the small ball , which is moving downward with identical speed vb at that instant. Immediately after the collision, the small ball moves upward with speed vS and the large ball has speed vL=0m/s .

Determine the height h (in meters) that the small ball rises above its lowest position.

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A 12kg stone slides down a snow-covered hill h=10m, leaving point A with a speed of 1.6m/s.

There is no friction on the hill between points A and B, but there is friction on the level ground at the bottom of the hill, between B and the wall.
After entering the rough horizontal region, the stone travels 35m and then runs into a very long, light spring with k=2,947N/m force constant

The coefficients of kinetic and static friction between the stone and the horizontal ground are 0.14 and 0.87, respectively.

How far will the stone compress the spring?

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A 573N archer (with all he holds) while on a frozen, essentially frictionless pond shoots a 297g arrow at 83m/s.

The archer holds tight to the bow after firing it.

Find the | magnitude | of the recoil velocity of the archer if he fires the arrow horizontally.

Each Problem should take no more than 10 minutes to solve and possibly an extra 2/3 for explaining.