Question

For this question (Determine the velocity of the 60 kg block A if the two blocks are released from rest and the 40 kg block B moves 0.6 m up the in cline. The coefficient of kinetic friction between both blocks and the inclined planes is = 0.05.), how is T(2) = 110 V(a)^2 instead of T(2) = -50V(a)^2

Answer 1

Length of the cable is given as;

Differentiating both sides with respect to time;

NOTE: The kinetic energy does not depend upon the direction (or the sign) of the velocity. It doesn't matter whether the velocity is left, right, up or down, kinetic energy will always be positive. Why? Because kinetic energy is given as;

Note that mass is always positive. Hence the only variable for which the sign changes is the velocity. Velocity can be positive or negative, but since WE SQUARE THE VELOCITY, hence no matter whether the velocity is positive or negative, once we SQUARE IT the final sign becomes POSITIVE.

Remember,

and also

When you square a negative value, it also becomes positive value. Minus multiply Minus = Plus.

Now, let's calculate the kinetic energy.

Now remember, when we take square of (-2v_A) it will become positive (and not negative). Hence,

...(Answer)