Home
Class 11
PHYSICS
A body constrainedto move along the z-ax...

A body constrainedto move along the z-axis of a co-ordinate system is subjected to a constant force `vec(F)` given by `vec(F)=-hat(i)+2hat(j)+3hat(k)` newton where `hat(i),hat(j)`and `hat(k)` represent unit vectors along x-,y-,and z-axes of the system, respectively.Calculate the work done by this force in displacing the body through a distance of `4m`along the z-axis.

Text Solution

Verified by Experts

Displacement=`4hat(k)`,Force: `vec(F)=-hat(i)+2hat(j)+3hat(k)`
Since work W is the scalar product of force and displacement,
`:.W=(-hat(i)+2hat(j)+3hat(k)).4hat(k)`
`= -4(hat(i).hat(k))+8(hat(j).hat(k))+12(hat(k).hat(k))=12J`
`[Because hat(i).hat(k)=0=hat(j).hat(k)` and `hat(k).hat(k)=1]`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise 3.1|19 Videos

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise 3.2|13 Videos

  • TRAVELLING WAVES

    CENGAGE PHYSICS|Exercise Integer|9 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Archives (integer)|4 Videos

Similar Questions

Explore conceptually related problems

A body constrained to move along the Z-axis of a co-ordinate system is subject to a constant forece vec F=-hat i+2hatj+3hatk , where hati, hatj,hatk are unit vectors along the X-,Y- and Z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the Z-axis ?

If vec(P)=hat(i)+hat(j)-hat(k) and vec(Q)=hat(i)-hat(j)+hat(k) , then unit vector along (vec(P)-vec(Q)) is :

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+hat(j)+hat(k) are two vectors, then the unit vector is

A body is constrained to move along z-axis of the co-ordinate system is being applied by a constant force vec(F)=(2hat(j)+3hat(j)+4hat(k)) . Find the work done by this force in moving the body over a distance of 5m along z-axis.

The angle which the vector vec(A)=2hat(i)+3hat(j) makes with the y-axis, where hat(i) and hat(j) are unit vectors along x- and y-axis, respectively, is

Two constant forces vec(F)_(1) = 6hat(i) +3hat(j)-hat(k) and vec (F)_(2) = 3hat(i) - 2hat(j) +hat(k) are acting upon a body along the same direction . Calculate the work done by these forces if the body is displaced from the point (2,1,2) to (3,-4,-5) .

If hat(i), hat(j) and hat(k) are unit vectors along x,y and z-axis respectively, the angle theta between the vector hat(i) + hat(j) + hat(k)" ""and vector" hat(j) is given by

Show that If vec(a)=x hat(i)+2hat(j)-z hat(k) and vec(b)=3hat(i)-y hat(j)+hat(k) are two equal vectors, then x+y+z=0 .

If hat(i), hat(j) and hat(k) represent unit vectors along the x, y and z axes respectively, then the angle theta between the vectors (hat(i) + hat(j) + hat(k)) and (hat(i) + hat(j)) is equal to :

The vector component of vector vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k) along vector vec(B) = hat(i) + hat(j) + hat(k) is