Question

A force represented by vector i-4j+3k acts
on body whose position vector with respect to
the axis of rotation is r=2j+5k. The torque
acting on the body is​

Answer 1

Answer:

$\boxed{ T = 26i + 5j + 2k }$

Explanation:

Given

F = i - 4 j + 3 k [/tex]

$r = 2 j + 5 k$

To Find

Torque

Solution

We know that

$\boxed{T = F \times r }$

$T = (i - 4 j + 3 k) \times (2 j + 5 k )$

As we know

Cross product of the vectors,

$\boxed{ a \times b = (a_{3}b_{2}-a_{2}b_{3})i -(a_{3}b_{1}-a_{1}b_{3})j + (a_{1}b_{2}-a_{2}b_{1})k}$

Putting the values

$T = [(3)(2)-(-4)(5)]i -[(3)(0)-(1)(5)]j + [(1)(2)-(-4)(0)]k$

$T = (6+20)i -(-5)j + (2)k$

$T = 26i + 5j + 2k$

$\pink{\mathbb{NOTE:-}}$

You can also prefer Det. product method to find the cross product of the vectors

Answer 2

The torque acting on the body is ( 26i + 5j - 2k ) N-m.

Given: A force represented by vector i - 4j + 3k.

position vector concerning the axis of rotation is r = 2j + 5k.

To Find: The torque acting on the body

Solution:

• Torque is the tendency of a force to rotate a body to which it is applied along the axis of rotation.

• We know that the formula for calculating torque is,

            T = r x F    [ where T = torque, F = force, r = position vector ]

• We need to perform cross product between the position vector and the force.

According to the given information,

r =  2j + 5k and F = i - 4j + 3k, Performing cross product of the vectors,

          T    = r x F

                = $\left[\begin{array}{ccc}i&j&k\\0&2&5\\1&-4&3\end{array}\right]$

                = i ( 6 + 20 ) - j ( 0 - 5 ) + k ( 0 - 2 )

                = ( 26i + 5j - 2k ) N-m

Hence, the torque acting on the body is ( 26i + 5j - 2k ) N-m.

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