1) Define work. When is work said to be done by a force ? 2) State the condition when the work done by a force is (a) positive, (b) negative. 3) Explain: The work done by a fielder when he takes a catch in a cricket match, is negative. 4) Derive the relation between joule and erg. Numericals : 1) A body, when acted upon by a force of 10 N, gets displaced by 0.5 m. Calculate the work done by the force, when the displacement is (i) in the direction of force, (ii) at an angle of 600 with the force and (iii) normal to the force. (g = 10 ms-2 ) 2) A boy of mass 40 kg climbs up the stairs and reaches the roof at a height 8 m in 5 s. Calculate (i) the force of gravity acting on the boy, (ii) the work done by him against the force of gravity, (iii) the power spent by the boy. (g = 10 ms-2 )
Answers
Work is said to be the energy provided to a body, by the action of an external force. Mathematically, it is the dot product of force and displacement, F•s , or FScos(a), where a is the angle between force and displacement.
The work done by a force is positive, when the angle between the two vectors is acute. ie, when cos(a) is positive
The work done by the force is negative when angle 'a' is greater than 180.
When a fielder takes a catch, the normal reaction of the players hands on the ball is opposite to the motion that the ball makes when the fielder catches it ( hands move backwards when catching) Thus, angle is obtuse and work is negative.
Joule is an SI unit, erg is a CGS unit. Please see attachment for derivation and numericals.
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