Complete Question
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Answer:
The expression is [tex] W_F = \frac{1}{2} * m * v__{{B}}} ^2 - mgh [/tex]
Explanation:
Generally the work energy theorem is mathematically represented as
[tex]PE_A + W_F = KE_B[/tex]
Here [tex]PE_A[/tex] is the potential energy at A which is mathematically represented as
[tex]PE_A = mgh[/tex]
And [tex]KE_B[/tex] is the kinetic energy at B which is mathematically represented as
[tex]KE_B = \frac{1}{2} * m * v__{{B}}} ^2[/tex]
So
[tex] mgh + W_F = \frac{1}{2} * m * v__{{B}}} ^2[/tex]
=> [tex] W_F = \frac{1}{2} * m * v__{{B}}} ^2 - mgh [/tex]
The expression for the work done by friction as the block slides from A to B will be [tex]W_F = \frac{1}{2}mv_b^2 -mgh[/tex].
Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.
Work may be zero, positive and negative.it depends on the direction of the body displaced. if the body is displaced in the same direction of the force it will be positive.
When the block of mass m is released from point A and slides down to point B, According to the work-energy theorem.
[tex]\rm W_f = = \frac{1}{2} mv_A^2-mgh \\\\[/tex]
The relation between potential energy, kinetic energy, and the work done by friction is given as;
[tex]\rm PE_A +W_F =KE_B[/tex]
The potential energy at point A on height his;
[tex]\rm PE_A=mgh[/tex]
The kinetic energy and point B will be;
[tex]\rm KE_B=\frac{1}{2} mv_B^2[/tex]
By putting the data in the work-energy theorem equation we get;
[tex]\rm mgh+ W_F = \frac{1}{2} v_B^2 \\\\ W_F = \frac{1}{2}mv_b^2 -mgh[/tex]
hence the expression for the work done by friction as the block slides from A to B will be [tex]W_F = \frac{1}{2}mv_b^2 -mgh[/tex].
To learn more about the work done refer to the link ;
https://brainly.com/question/3902440
