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Laws Of Motion

Question
CBSEENPH11020796

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 30° with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is

  • 48 N

  • 24 N

  • 12 N

  • 96 N

Solution

B.

24 N

The vector OA with rightwards arrow on top represents the momentum of the object before the collision, and the vector OB with rightwards arrow on top that after the collision. The vector AB with rightwards arrow on top represents the change in momentum of the object increment straight P with rightwards arrow on top.


As the magnitudes of  OA with rightwards arrow on top space and space OB with rightwards arrow on top are equal, the components of OA with rightwards arrow on top space and space OB with rightwards arrow on top along the wall are equal and in the same direction, while those perpendicular to the wall are equal and opposite. Thus, the change in momentum is due only to the change in direction of the perpendicular components.
Hence,  increment straight p space equals space OB space sin space 30 degree space minus space left parenthesis negative OA space sin space 30 degree right parenthesis
                    equals mv space sin space 30 degree space minus space left parenthesis negative mv space sin space 30 degree right parenthesis
equals 2 space mv space sin space 30 degree
Its time rate will appear in the form of average force acting on the wall.
 therefore space space space space space space space space space straight F space cross times space straight t space equals space 2 mv space sin space 30 degree
or space space space space space space space space space space space space space space straight F space equals space fraction numerator 2 mv space sin space 30 degree over denominator straight t end fraction
   Given comma space straight m space equals space 0.5 space kg comma space space straight v space equals space 12 space straight m divided by straight s comma space space space straight t equals space 0.25 space straight s
space space space space space space space space space space straight theta space equals space 30 degree
Hence comma space space space straight F space equals space fraction numerator 2 cross times 0.5 cross times 12 space sin space 30 degree over denominator 0.25 end fraction space equals space 24 space straight N