A particle moves from a point r 1-2 m i -3 m j to another point r 2-3 m i -2 m j during which a certain fore F -5 N i -5 N j acts on it- Find the work done by the force on the particle during the displacement-

Given,r_1=2i+3j r_2=3i+2j So, displacement vector is given by, r=r_2 r_1 =(3i+2j) (2i+j) =i j Again F=5i+5j So, work done =F.S=5×1+5( 1)=0 ...

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Standard XII

Physics

Work Done as Dot Product

A particle mo...

Question

A particle moves from a point $_{1} = (2 m) \to i + (3 m) \to j$ to another point $_{2} = (3 m) \to i + + (2 m) \to j$ during which a certain fore $\to F = (5 N) \to i + (5 N) \to j$ acts on it. Find the work done by the force on the particle during the displacement.

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Solution

Given, $_{1} = 2 \to i + 3 \to j$

$_{2} = 3 \to i + 2 \to j$

So, displacement vector is given by,

$\to r =_{2} -_{1}$

$= (3 \to i + 2 \to j) - (2 \to i + \to j)$

$= \to i - \to j$

Again $\to F = 5 \to i + 5 \to j$

So, work done $= \to F . \to S = 5 \times 1 + 5 (- 1) = 0$

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Similar questions

A particle moves from a point ${\to r}_{1} = 2^i + 3^j (m)$ to another point ${\to r}_{2} = 3^i + 2^j (m)$ during which a certain force $\to F = 5^i + 5^j$ acts on it. Find the work done by the force on the particle during the displacement.

Q. A particle moves from a point

_{1} = (2^i + 3^j)

to another point

_{2} = (3^i + 2^j)

during which a certain force

\to F = (5^i + 5^j)

acts on it. Calculate work done by the force on the particle during this displacement.

Q. A particle moves from a point

{\underset{r}{\to}}_{1} = (2 m) \underset{i}{\to} + (3 m) \underset{j}{\to}

to another point

{\underset{r}{\to}}_{2} = (3 m) \underset{i}{\to} + (2 m) \underset{j}{\to}

acts on it. Find the work done by the force on the particle during the displacement.

Q. Work done by a force

F = (^i + 2^j + 3^k) N

acting on a particle in displacing it from the point

_{1} =^i +^j +^k

to the point

_{2} =^i -^j + 2^k

Q. Work done when a force

\to F = (^i + 2^j + 3^k) N

acting on a particle displaces it from the point

r_{1} = (^i +^j +^k)

to the point

r_{2} = (^i -^j + 2^k)

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A particle moves from a point →r1=(2 m)→i+(3 m)→j to another point →r2=(3 m)→i++(2 m)→j during which a certain fore→F=(5 N)→i+(5 N)→j acts on it. Find the work done by the force on the particle during the displacement.

Given,→r1=2→i+3→j →r2=3→i+2→j So, displacement vector is given by, →r=→r2−→r1 =(3→i+2→j)−(2→i+→j) =→i−→j Again →F=5→i+5→j So, work done =→F.→S=5×1+5(−1)=0

A particle moves from a point $_{1} = (2 m) \to i + (3 m) \to j$ to another point $_{2} = (3 m) \to i + + (2 m) \to j$ during which a certain fore $\to F = (5 N) \to i + (5 N) \to j$ acts on it. Find the work done by the force on the particle during the displacement.

Given, $_{1} = 2 \to i + 3 \to j$

$_{2} = 3 \to i + 2 \to j$

So, displacement vector is given by,

$\to r =_{2} -_{1}$

$= (3 \to i + 2 \to j) - (2 \to i + \to j)$

$= \to i - \to j$

Again $\to F = 5 \to i + 5 \to j$

So, work done $= \to F . \to S = 5 \times 1 + 5 (- 1) = 0$