Question

.A particle moves along the z axis from z=0 to z=4 under the influence of a force F = 3z2- z + 5 .Calculate the work done by the force.

Answer 1

Work done by the force is 76 J

Given

A particle moves along the z axis from z=0 to z=4 under the influence of a force F = 3z²- z + 5

To Find

Work done

Knowledge Required

$\displaystyle \bf \green{\bigstar\ \; W=\int_a^{b}Fdz}$

Solution

• F = 3z² - z + 5
• a = 0
• b = 4

$\bf W=\displaystyle{\int_0^4} (3z^2-z+5)dz\\\\\to \rm W=\left[ z^3-\dfrac{z^2}{2}+5z \right]_0^4\\\\\to \rm W=\left[4^3-\dfrac{4^2}{2}+5(4)\right]-[0]\\\\\to \rm W=64-8+20\\\\\to \bf \green{W=76\ J\ \; \bigstar}$

So , Work done by the force is 76 J

Answer 2

Answer:

Work done by the force is 76 J

Given

A particle moves along the z axis from z=0 to z=4 under the influence of a force F = 3z²- z + 5

To Find

Work done

Knowledge Required

\displaystyle \bf \green{\bigstar\ \; W=\int_a^{b}Fdz}★ W=∫

a

b

Fdz

Solution

F = 3z² - z + 5

a = 0

b = 4

\begin{gathered}\bf W=\displaystyle{\int_0^4} (3z^2-z+5)dz\\\\\to \rm W=\left[ z^3-\dfrac{z^2}{2}+5z \right]_0^4\\\\\to \rm W=\left[4^3-\dfrac{4^2}{2}+5(4)\right]-[0]\\\\\to \rm W=64-8+20\\\\\to \bf \green{W=76\ J\ \; \bigstar}\end{gathered}

W=∫

0

4

(3z

2

−z+5)dz

→W=[z

3

−

2

z

2

+5z]

0

4

→W=[4

3

−

2

4

2

+5(4)]−[0]

→W=64−8+20

→W=76 J ★

So , Work done by the force is 76 J