How Do You Calculate the Component of Force in a Given Direction?

[ness9660]

First,

For a 3kg object, displacement is given by 6i+3j-4k with a constant force F=2N i + -1N J + 7N k.

Ive found the total work, but the next question is ' Find the component of F in the direction of this displacement. Answer in units of N. '

Im really confused as to what is even being asked here. It wants single numerical answer, but it seems as though its asking for the x,y and z compenents of the force. The most logical choice seems that it wants magnitude of the Force, but this is wrong.



Secondly,

A civil engineer is asked to design a curved
section of roadway that meets the following
conditions:
With ice on the road, when the coffcient of
static friction between the road and rubber is
0.25, a car at rest must not slide into the ditch
and a car traveling less than 50 km/h must
not skid to the outside of the curve.
The acceleration of gravity is 9.81 m/s^2

At what angle should the road be banked?
Answer in units of degress.


This problem completely leaves out the radius, and without radius I am unsure how to solve this, can anyone offer some help as how to go about solving this?

 

[Astronuc]

First - the problem is to find the F component in the direction of 6i+3j-4k.

Find the unit vector in the direction of 6i+3j-4k, and then . . . .



Secondly - use the static part of the problem to find the banking angle.

With the banking angle, determine the radius that a car can travel without sliding to the outside of the curve.