Question 1: (June 2008 Q4)
- Draw a diagram with the forces in the horizontal and vertical direction (remember the normal reaction and frictional force)
- If unsure what direction to mark the frictional force, it doesn’t matter, because if you find your final solution is negative, it was in the opposite direction
- Resolve horizontally
- Use Fmax = uR
- Resolve vertically to find R and use your Fmax from part (i)
Question 2: (Jan 2012 Q2)
- Consider what information you have been given …. time (t), final velocity (v) and displacement (s).
- Consider what you are trying to find…. acceleration (a)
- Is there a formula connecting t, v, s and a?
- When writing deceleration, give it as a magnitude… i.e. ignore the negative sign from acceleration.
- Use F=ma
- If you know the weight, how could you find the mass?
- Once you find the frictional force, use Fmax = uR to find u (u is meant to be mu)
Question 3: (Jan 2012 Q6)
- You are given u and v.
- Find a by using F=ma (resolve forces)
- Then find s by using the formula that connects v, u, a and s
- Consider the return journey. u = 0 and s will be the answer from (i)
- Find a again by using F=ma
- Then find t by using the equation of motion that connects s, u, a and t
I took this photograph whilst on holiday in Barcelona. It is the roof of a market.
What do you notice about the shapes on the roof?
Why do you think the shapes fit together perfectly?
How do you think you could show this mathematically?
Where else have you seen patterns that tessellate? Art?
Which other polygons will tessellate?