Scalars and Vectors
Definitions
- Vector: A vector is quantity with a direction and magnitude/size.
- Scalar: A Scalar is a quantity without a direction, only magnitude/size.
- Force: A push or a pull that acts on an object due to an interaction with another object.
- Contact force: The objects are (sort of) physically friction.
- Non-contact: The objects are physically apart.
Resolving Vectors into componants
Using Trigonometry:
- \(\sin\theta=\frac{F_{v}}{F}\)
- \(\cos\theta=\frac{F_{h}}{F}\)
This can be rearranged to:
- \(F_{v}=F\sin\theta\)
- \(F_{h}=F\cos\theta\)
Resolving vectors questions
- \(50\times \sin 30=25N\) vertical; \(50\times \cos30=25\sqrt{ 3 }N\) horizontal.
- \(50\times \sin 15=\frac{25\sqrt{ 6 }-25\sqrt{ 2 }}{2}N\) vertical; \(50\times \cos 15=\frac{25\sqrt{ 6 }+25\sqrt{ 2 }}{2}N\) horizontal.
- \(25\times \sin15=\frac{25\sqrt{ 6 }+25\sqrt{ 2 }}{4}N\) vertical; \(25\times \cos15=\frac{25\sqrt{ 6 }-25\sqrt{ 2 }}{4}N\) horizontal.
- \(50\times \sin 30=25N\) vertical; \(50\times \cos30=25\sqrt{ 3 }N\) horizontal.
- \(20\times \sin15=5\sqrt{ 6 }-5\sqrt{ 2 }N\) vertical; \(20\times \cos15=5\sqrt{ 6 }+5\sqrt{ 2 }N\)
Resolving on a slope
More resolving on a slope
- To find weight, use W=mg
- Use trig to resolve the forces into horizontal and vertical componants
- Use \(W=\sin\theta\) and \(W=\cos\theta\) to do this.
- Now you can use \(F=ma\) to find the accelleration.