Question

to maintain same speed shouldnt work done be 0

Answer 1

Yes, to maintain the same speed, the net work done on the object should be 0.

Answer 2

Explanation of the Solution:

The relationship between work done and an object's speed is described by the Work-Energy Theorem.

1. Work-Energy Theorem: This theorem states that the net work ($W_{net}$) done on an object is equal to the change in its kinetic energy ($\Delta KE$).

   $W_{net} = \Delta KE = KE_{final} - KE_{initial}$

2. Kinetic Energy and Speed: Kinetic energy ($KE$) is given by the formula $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the speed of the object.

3. Constant Speed Implication: If an object maintains the same speed ($v = \text{constant}$), then its kinetic energy ($KE = \frac{1}{2}mv^2$) also remains constant.

4. Change in Kinetic Energy: Since the kinetic energy is constant, the change in kinetic energy ($\Delta KE$) is zero.

   $\Delta KE = KE_{final} - KE_{initial} = 0$

5. Conclusion on Net Work Done: From the Work-Energy Theorem, if $\Delta KE = 0$, then the net work done ($W_{net}$) on the object must also be zero.

   $W_{net} = 0$

Therefore, to maintain the same speed, the net work done on the object must be zero. It's important to distinguish this from work done by individual forces; individual forces can still do non-zero work, but their effects balance out, resulting in zero net work.