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(i) Two bodies of masses m(1)(m(2) gt m(...

(i) Two bodies of masses `m_(1)(m_(2) gt m_(1))` are connected by a light inextensible string which passes through a smooth fixed pulley. What is the instantaneous power delivered by an external agent to pull `m_(1)` with constant velocity `vec(V)`?

(ii) A small body of mass m is located on a horizontal plane at any point O. The body acquires a horizontal velocity `v_(0)` . Find the mean power developed by the friction force during the motion, if the coefficient of friction `mu=0.27, m=1.0` kg and `v_(0)=1.5m//s`.

Text Solution

Verified by Experts

(i) `P=vec(F).vec(v)=(m_(2)-m_(1))g.v cos 0^(@)=(m_(2)-m_(1))gv`.
(ii) `bar(P)=1/T int_(0)^(T)P.dt, bar(P)=1/T int_(0)^(T) mu mg(v_(0)- mu gt )dt ` (numerically)
`=(mu mg)/(T)(v_(0)T-(mu g T^(2))/(2))=mu mg(v_(0)-(mu gT)/(2))`.
where `T=(v_(0))/(mu g) rArr bar(P)=(mu mgv_(0))/(2)=(0.27xx1xx10xx1.5)/(2)`
`rArr bar(P)=2.025` watts.
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