A body constrained to move along the y-axis i | vedclass

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

Question

(B) The force acting on the body is given by $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} 	ext{ N}$.Since the body is constrained to move along the $y$-

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) The force acting on the body is given by $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} 	ext{ N}$.Since the body is constrained to move along the $y$-axis for a distance of $4 	ext{ m}$,the displacement vector is $\vec{d} = 4\hat{j} 	ext{ m}$.The work done $W$ by a constant force is defined as the dot product of the force vector and the displacement vector: $W = \vec{F} \cdot \vec{d}$.Substituting the values: $W = (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (4\hat{j})$.Using the dot product properties ($\hat{i} \cdot \hat{j} = 0$,$\hat{j} \cdot \hat{j} = 1$,$\hat{k} \cdot \hat{j} = 0$):$W = (-1 	imes 0) + (2 	imes 4) + (3 	imes 0) = 8 	ext{ J}$.Thus,the work done is $8 	ext{ J}$.

$A$ body constrained to move along the $y$-axis is subjected to a constant force $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N}$. The work done by this force in moving the body a distance of $4 \text{ m}$ along the $y$-axis is ............... $J$.

Similar Questions

$A$ body moves a distance of $10 \, m$ along a straight line under the action of a force of $5 \, N$. If the work done is $25 \, J$,the angle which the force makes with the direction of motion of the body is.....$^o$

$A$ force of magnitude $50\, N$ acting along $\hat{i} + \hat{j} + \hat{k}$ displaces a point mass from $(5, 9, 7)$ to $(4, 8, 6)$. The work done by this force during this displacement is:

$A$ heavy object and a light object are placed on the same surface. If the same force is applied to both for the same displacement,on which object is more work done by the force?

$A$ horizontal force of $5 \,N$ is required to maintain a velocity of $2 \,m/s$ for a block of $10 \,kg$ mass sliding over a rough surface. The work done by this force in one minute is $J$.

$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $u$. The force on the body is $mv^2/r$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module