Figure shows a light, inextensible string attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the string is pulled over a small pulley, of n

Question

Figure shows a light, inextensible string attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the string is pulled over a small pulley, of negligible mass and friction and fixed at height $h = 3 m$ from the ground level. The cart slides from $x_{1} = 33 m$ to $x_{2} = 4 m$ and during the move, tension in the string is kept constant 50 N. Find change in kinetic energy of the cart in joules. (Use $3 = 1.7$ )

TestHub · Accepted Answer

Work by the constant tension = T times the string length pulled over the pulley: $W = T (l_{1} - l_{2})$ .

$l_{1} = x_{1}^{2} + h^{2} = 27 + 9 = 6 m, l_{2} = 16 + 9 = 5 m$ .

$Δ K = 50 \times (6 - 5) = 50 J$ . Answer: 50.

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