Question

A particle moves along the X-axis from
x = 0 to x = 5 m under the influence of
a force given by F = 7 - 2x + 3x2. Find
the work done in the process.​

Answer 1

Explanation:

F = 7-2x+ 6x

= 7- 4x

0 = 7-4x

4x = 7

x = 7/4 =1.75

F = 7-2×1.75 +6×1.75

F= 7 + 7 = 14

w = Force in dispalcement

=14 × 5

= 70

Answer 2

Given: A particle moves along the X-axis from x = 0 to x = 5 m under the influence of a force given by F = 7 - 2x + 3x².

To find: the work done in the process.

Solution: For a variable force, we know that work done is given by:

                  ∫dW = ∫F. ds

Putting the given values in the formula, we get:

                ∫dW = ∫⁵₀ (3x² - 2x + 7) dx

                        = 3(x3/3)⁵₀ - 2(x2/2)⁵₀ + 7(x)⁵₀

                        = 125 - 25 + 35

                        = 135 J.

Hence, the work done in the process is 135 J.