By Pat Bryden
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Additional resources for Mechanics 1
Example text
In modelling the motion of the ball and stone it is assumed that each object moves in a straight line with a constant downward acceleration of magnitude 10 ms~2. The stone is thrown with initial speed of 15 ms"1 and is hs metres above the ground t seconds later. (i) Draw a diagram of the ball and stone before they collide, marking their positions. (ii) Write down an expression for hs at time t. (iii) Write down an expression for the height h^ of the ball at time t. (iv) When do the ball and stone collide?
Make sure that your units are compatible. 3 Using a mathematical model Make simplifying assumptions by deciding what is most relevant. For example: a car is a particle with no dimensions a road is a straight line with one dimension acceleration is constant. Define variables and set up equations. Solve the equations. Check that the answer is sensible. If not, think again. 36 3 Forces and Newton's laws 3 of motion Nature and Nature's Laws lay hid in Night. God said. Let Newton be! and All was Light.
Which of these answers are likely to need adjusting to take account of air resistance? Would you expect your answer to be an over- or underestimate? 4 A car starting from rest at traffic lights reaches a speed of 90 km h"1 in 12s. Find the acceleration of the car (in ms~ 2 ) and the distance travelled. Write down any assumptions that you have made. 5 A top sprinter accelerates from rest to 9 ms"1 in 2 s. Calculate his acceleration, assumed constant, during this period and the distance travelled.