A body is acted upon by a constant force N

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A body is acted upon by a constant force

\vec F=4\mathbf i-3\mathbf j+12\mathbf k

N. While moving from point

A

to point

B

, the body experiences a displacement that is known to be along the direction of the vector

\vec a=2\mathbf i+\mathbf j+2\mathbf k

. (i) Let the displacement from

A

B

\vec d=\lambda\vec a

metres, where

\lambda

is a positive real number. Express

\vec d

in component form in terms of

\lambda

. (ii) Given that the work done by the force in moving the body from

A

B

60

J, determine the value of

\lambda

and hence write the exact displacement vector. (iii) Using your answer to part (ii), calculate the angle between

\vec F

and

\vec d

(correct to the nearest degree).