$29.$ A ball is dropped vertically onto a floor and rebounds. The graph shows how the momentum of the ball varies with time. The direction upward's is positive.

The ball falls freely between $0$ and $0\mathrm{.}5$ s $.$ Air resistance is negligible.

a$.$ Calculate:

i$.$ the weight of the ball

ii$.$ the speed of the ball just before impact.

b$.$ The ball is in contact with the floor for a time of $0\mathrm{.}10$ s $.$

Determine the magnitude of the average contact force between the floor and the ball.

Practice questions

$49.$ A stone of mass $0\mathrm{.}25$ kg attached to the end of a string is moving in a vertical circle of radius $0\mathrm{.}80$ m at a constant speed. The string will break if the tension in it exceeds $10$ N $.$

a$.$ Explain whether the string is more likely to break when the stone passes the lowest or the highest point of the path.

b$.$ Calculate:

i$.$ the minimum speed of the stone so that the string remains taut at the highest point

ii$.$ the maximum speed of the stone so that the string doesn't break.