The work done in moving an object from the or | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We know that the work done $W$ is given by the dot product of force $\vec{F}$ and displacement $\vec{d}$.Given,force $\vec{F} = 2 \hat{i} - \hat{j

Vedclass · Accepted Answer

$9 	ext{ units}$

Vedclass · Answer

(B) We know that the work done $W$ is given by the dot product of force $\vec{F}$ and displacement $\vec{d}$.Given,force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$.The object moves from the origin $(0, 0, 0)$ to the position vector $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$,so the displacement $\vec{d} = \vec{r} - 0 = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$.Using the property of dot product $\hat{i} \cdot \hat{i} = \hat{j} \cdot \hat{j} = \hat{k} \cdot \hat{k} = 1$ and $\hat{i} \cdot \hat{j} = \hat{j} \cdot \hat{k} = \hat{k} \cdot \hat{i} = 0$,we calculate:$W = \vec{F} \cdot \vec{d} = (2 \hat{i} - \hat{j} - \hat{k}) \cdot (3 \hat{i} + 2 \hat{j} - 5 \hat{k})$$W = (2 	imes 3) + (-1 	imes 2) + (-1 	imes -5)$$W = 6 - 2 + 5 = 9 	ext{ units}$.

The work done in moving an object from the origin to a point whose position vector is $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$ is:

Similar Questions

$A$ body,constrained to move in the $Y$-direction,is subjected to a force given by $\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k})\,N$. What is the work done by this force in moving the body a distance $10\,m$ along the $Y$-axis?

Calculate the work done by a car against gravity in moving along a straight horizontal road. The mass of the car is $400\,kg$ and the distance moved is $2\,m$. (in $,J$)

$A$ force $\vec F = 2\hat i - 3\hat j + 7\hat k \text{ (N)}$ acts on a particle which undergoes a displacement of $\vec S = 7\hat i + 3\hat j - 2\hat k \text{ (m)}$. Calculate the work done by the force in $J$.

$A$ man carries a load on his head through a distance of $5 \,m$. The maximum amount of work is done when he ..........

If a person is pushing a box inside a moving train,the work done in the frame of the earth will be: (where $\vec{s}$ is the displacement of the box in the train and $\vec{s}_0$ is the displacement of the train relative to the ground)

Vedclass Test Series

Exam Paper Generator

Online Exam Module