Mechanics1 Worked solutions June 2006 paper

Link to worked solutions for June 2006 M1 paper:

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZTQyZGU3NDUtN2QzNy00MDE1LTg1YzAtODM1ZWRmYmVjNzQx&hl=en

Notes to support worked solutions:

1. (a) the gradient of a speed-time graph is acceleration so a straight line (so constant gradient) will represent constant acceleration
(b) so a horizontal line has gradient = 0 so acceleration = 0 so constant speed
(c) area under a speed time graph represents distance travelled

2. (a) considering the whole system the inital momentum will be equal to the final momentum - remember momentum = mass x velocity - make sure directions of velocities are used correctly - in this case right is defined as positive - the only unknown v is found - the fact that it is found to b positive shows that the direction is to the right so the direction of the particle is unchanged
(b) considering just a single particle the change in momentum (final momentum - initial momentum) is equal to the impulse acting on it

3.(a) for the journey A to B, s&u&t are known so a can be found
(b) for the whole journey A to C, s&u are known and a was found in (a) so v can be found
(c) again using whole journey A to C the only remaining unknown t can be found - don't forget to subtract 2 seconds to give the required answer of the time from B to C

4. aside about the angle of elevation - tan of the angle is given as 3/4 which could be used to find the angle although this would be a long decimal - it is simpler for the question to find that sin of the angle = 3/5 and cos of the angle = 4/5 gby using a 3,4,5 triangle
(a) perpendicular to the plane finds the normal reaction
parallel to the plane finds the frictional force
these are combined to find the coefficient of friction
(b) frictional force is now up the slope althought its size will not have changed from (a) because the normal reaction won't have changed because no forces perpendicular to the slope have changed
- find the resultant force down the slope (ie parallel to the slope)
- use F=ma to find the acceleration down the slope

5. (a) the information given about the tensions and just using up=down lets us find the size of the tensions
(b) the diagram was set up with x being half the length AB - by taking moments about this length can be found
(c) taking moments about B eliminates the unknown W so the tension can be found then up = down finds W

6. (a) considering whole system (tensions cancel each other out) and using resultant force = mass x acceleration the acceleration is found
(b) by considering just the car the tension can be found (could have equally considered just the trailer
(c) as diagram shows the only forces acting on car are the engine and the resistance - again use F = ma to find the acceleration - followed by suvat to find the distance
(d)

7. (a) speed is the magnitude of the velocity vector so just use pythagoras on the i and j values
(b) make sure the correct angle is identified for the bearing (clockwise from north)
(c) the position after 3 hours is the start position plus 3 lots of the velocity
(d) position after 2 hours is the start position plus 2 lots of the velocity
- the new velocity just adds 5 to the j every hour
(e) to be due east of a point means having the same vertical distance (ie the j component as that point) - be careful translating 1.2 hours into 1 hour and 12 minutes (12 mins is 2/10 of an hour)
(f) 2 hours after the new velocity just adds 10 the the j
the displacement vector from R is found by subtracting R
then the distance is the magnitude of the displacement vector so just use pythagoras on the i and j components