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a cart moves on a smooth horizontal surface due to an external constant force F the intial mass of the the cart is M and the velocity is 0. sand falls on the cart with negligible velocity at constant rate U kg/s and sticks to the cart . find the velosity of the cart at the time T . ALSO FIND THE RATE OF INCREASE OF THE KINETIC ENERGY OF THE CART.
please answer the above question in detail
at any time ,
a = F/(M+m),
where m = Ut, [dm/dt = U]
now writing acceleration as dv/dt
dv/dt = F/(M+Ut)
now integrating both sides ,we get
V = F*ln(1+Ut/M)/U ....here initial conditions are at t= 0,V=0, m = 0
now k.E , k = 0.5*(M+m)V2
rate of change of kE is dk/dt
dk/dt = 0.5*U*V2 + 0.5*(M+m)*2*V*dv/dt
dk/dt = 0.5*U*V2 + (M+m)*V*dv/dt
now just substituting the values of V , m, dV/dt
we can get the rate of change of kE
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