Question

A constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k}$ N has a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k}$ m in 2 second. The work done and the power are respectively ______.

• A. 20 joule, 10 watt
• B. 15 joule, 7.5 watt
• C. 13 joule, 6.5 watt
• D. 10 joule, 5 watt

Hint:

Dot products ($\cdot$) always result in a scalar (a single number), which makes perfect sense because Work and Energy are scalar quantities, possessing magnitude but no physical direction.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Work done is the dot product of force and displacement vectors ($W = \vec{F} \cdot \vec{r}$). Power is the rate of doing work ($P = W/t$).

Step 2: Formula Application:
$W = (3)(2) + (-2)(-3) + (-1)(-3)$. $W = 6 + 6 + 3 = 15$ J.

Step 3: Explanation:
Power $P = \frac{W}{t} = \frac{15}{2} = 7.5$ W.

Step 4: Final Answer:
Work done is 15 J and power is 7.5 W.