Figure shows a cord attached to a cart that can slide along a friction less horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height h = 1.20 m, so the cart slides from $x_{1} = 3.00 m$ to $x_{2} = 1.00 m$ . During the move, the tension in the cord is a constant 25.0 N. What is the change in the kinetic energy of the cart during the move?

Question

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Answer 1

We solve the problem using the work-kinetic energy theorem, which states that the change in kinetic energy is equal to the work done by the applied force, $Δ K = W$ .

In this problem, the work done is $W = F d$ , where F is the tension in the cord and d is the length of the cord pulled as the cart slides from $x_{1}$ to $x_{2}$ .

From the figure, we have

$d = x_{1}^{2} + h^{2} - x_{2}^{2} + h^{2}$

$= (3.00 m)^{2} + (1.20 m)^{2} - (1.00 m)^{2} + (1.20 m)^{2}$

$= 3.23 m - 1.56 m = 1.67 m$

which yields $Δ K = F d = (25.0 N) (1.67 m) = 41.7 J .$

Answer 2

We solve the problem using the work-kinetic energy theorem, which states that the change in kinetic energy is equal to the work done by the applied force,

Δ K = W

.

In this problem, the work done is

W = F d

, where F is the tension in the cord and d is the length of the cord pulled as the cart slides from

x_{1}

to

x_{2}

.

From the figure, we have

d = x_{1}^{2} + h^{2} - x_{2}^{2} + h^{2}

= (3.00 m)^{2} + (1.20 m)^{2} - (1.00 m)^{2} + (1.20 m)^{2}

= 3.23 m - 1.56 m = 1.67 m

which yields

Δ K = F d = (25.0 N) (1.67 m) = 41.7 J .

Four blocks of same mass connected by cords are pulled by a force $F$ on a smooth horizontal surface, as shown in figure. The tensions $T_{1}, T_{2}$ and $T_{3}$ will be
$F \leftarrow M T_{1} M T_{2} M T_{3} M$

A block is moved from rest through a distance of 4m along a straight line path.The mass of the block is 5 kg,and the force acting on it is 20 N.If the kinetic energy acquired by the block be 40J,at what angle to the path the force is acting:

A block of mass $2 k g$ is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force $F = 40 N$ . The kinetic energy of the particle increases $40 J$ in a given interval of time. Work done by tension is

Revise with Concepts

Work Energy Theorem

Work Energy Theorem - Problem L1

Four blocks of same mass connected by cords are pulled by a force F on a smooth horizontal surface, as shown in figure. The tensions T1​,T2​ and T3​ will be F←MT1​​MT2​​MT3​​M