Mechanics & properties of Matter
Homework 1

1. Acceleration due to gravity is measured six times under identical conditions.
   The values given are
   (9.72, 10.35, 9.41, 9.87, 10.29, 9.28) ms^-2.
   
   1. Calculate
      
      1. the mean value of the acceleration (1)
      2. the approximate random uncertainty. (1)
   2. State how this uncertainty could be reduced without altering the apparatus. (1)
   
   
2. A car travels 452 ± 0.5 m in a time of 27 ± 1 s.
   
   1. Calculate
      
      1. the average speed of the car (2)
      2. the percentage uncertainty for both distance and time. (2)
   2. State the percentage error in the value for the average speed. (1)
   
   
3. 
   The mercury bead in a thermometer splits making all of the readings too high.
   What type of uncertainty will this introduce to our measurements? (1)


4. A digital ammeter is used to measure the current flowing through a bulb.
   The display shows 0.28 A.
   Calculate a suitable reading uncertainty for this measurement. (1)


5. A pupil uses a metre stick to measure the length of a jotter and records it as 21.7 cm.
   Estimate the reading uncertainty and state it as a percentage of the measurement. (1)


6. A referee jogs round a football pitch from A to B and then from B to C.
   
   The total time taken is 100 seconds.
   
   1. By scale drawing or otherwise, find the resultant displacement.
      Magnitude and direction are required. (2)
   2. Calculate
      1. the average speed of the referee from A to C. (2)
      2. the average velocity of the referee from A to C. (2)
      3. the bearing that the referee would jog along to return back
         directly from C to A. (1)
      
      
7. Two ropes attached to tractors are used to pull on a large boulder.
   Each tractor exerts a force of 2000 N at 30° relative to East.
   
   By scale drawing or otherwise, find the resultant force produced by the ropes. (3)