Find the value of K if work done is zero for the force

F= =2i+5j and displacement

d = si-Kİ (Kis positive

To determine the value of K for which the work done is zero, we can use the formula for work done, which is given by the dot product of force and displacement.

Understanding the Components

Given:

• Force, F = 2i + 5j
• Displacement, d = si - Kİ

Calculating the Dot Product

The work done (W) can be expressed as:

W = F · d

Substituting the values:

W = (2i + 5j) · (si - Kİ)

Expanding the Dot Product

Now, we can calculate the dot product:

W = 2s - 5K

Setting Work Done to Zero

For the work done to be zero:

2s - 5K = 0

Solving for K

Rearranging the equation gives:

5K = 2s

K = (2s)/5

Conclusion

Thus, the value of K depends on the value of s. If s is known, you can substitute it into the equation to find K. Remember, K must be positive, so ensure that s is also positive for K to remain valid.