06 - Further Mechanics

Question 1

6. Explain why the energy was far higher than calculated 7TeV

Answer 1

At relativistic speeds the mass of proton increases

The equation Ek= P^2/2m is only valid at non-relativistic speeds

Question 2

6. Explains what happens to make the last ball bearing on the right subsequently move off with a large velocity

Answer 2

Magnet accelerates ball
Momentum is conserved in the collision
Since collisions are assumed to be elastic, KE is conserved so 3rd ball moves off with the same KE as incoming ball

Question 3

6. Explain why it is possible for a toy car to complete the loop without losing contact with the inside of the track

Answer 3

F= mv^2/r AND F=ma -> a-g
mg=mv^2/r
g=v^2/r
gr=v^2
v=root gr

Question 4

6.Explain why the car will slip off the curved part of the track if the car exceeds the maximum speed

Answer 4

A resultant force is required to maintain circular motion
This force is friction btwn car and the track
As v increased, F required is increased until it exceeds friction
Car slides off the track

Question 5

6. Identical cars
   one car on inner track , one car on outer track
   each car is raced at its highest speed for that lane

Explain why the outcome of the race is difficult to predict

Answer 5

inner lane covers a smaller distance with a smaller radius of curvature
maximum horizontal force is the same for both cars
maximum speed is greater for the car on the outside lane but the car has a greater distance to cover with a greater radius of curvature
outcome unclear