A STUDENT SWINGS A STOPPER OF MASS 0.32 KG IN A HORIZONTAL CIRCLE (PARALLEL TO THE FLOOR), AS SHOWN IN THE FIGURE.

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.

//////////////

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.

/////////////

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.

/////////

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.

////////////////////////

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?

/////////

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.