Download Getting Ready SPH4U Significant figures 1. Indicate the number of

Getting Ready
SPH4U
Significant figures
1. Indicate the number of significant figures for the numbers written below:
a) 1.002
b) 0.060
c) 4115000
d) 8.120.106
e) 4.9000.10-4
f) 989.9950
g) 1.00300
2. A desk has been measured to be 120.7 cm long and 50.456 cm wide.
a) determine the perimeter of the table and express the result with the correct
number of significant figures.
b) determine the area of the table and express the result with the correct number
of significant figures.
Uncertainty in measurements
3. Consider the desk from question 2.
a) What is the uncertainty in measurement of the table’s length and width?
b) What is the uncertainty in measurement of the table’s perimeter?
c) What is the percent uncertainty in measurement of the table’s length?
d) What is the uncertainty in the measurement of the table’s area?
4. In an investigation to measure the magnitude of the acceleration due to gravity
where the known value is 9.8 m/s2, group A gets 9.4 m/s2 and group B gets
9.7 m/s2.
(a) Determine the possible error in the value obtained by group A.
(b) Determine the percent possible error in the value obtained by group A.
(c) Determine the percentage error in the value obtained by group A.
(d) Determine the percentage difference between the values of the two groups.
Scientific Notation
5.Express each of the following numbers in scientific notation:
a) 627.4
b) 0.000365
c) 20001
d) 1.00067
e) 0.0067
6. Express each of the following numbers as simple numbers:
a) 31.65.10-3
b) 0.415.106
c) 1.00/(2.05.10-3)
d) 1.00/(43x103)
7. Add the following two numbers:
a) 1.234.105 + 4.2.104
Scalar and Vector quantities
Note: For vector directions we will use the same convention as described
in the book thus [30 N of E] means turn East and then turn 30 toward
North. The other convention is to write the same vector as follows [N70E]
which means turn North and then turn 70 toward East.
8. List four scalar and four vector quantities associated with motions and forces,
and for each indicate the SI units and a typical example.
9. Using the convention from the book and a protractor draw the following
displacement vector.
r
d  4 cm [34 N of E]
b) Calculate its dx and dy components.

r
10. Find the x and y components of a displacement vector d  4 cm [60 W of S].
Vector Addition and subtraction - part 1

11. a) Use a vector scale diagram (1 cm = 10km) to determine the magnitude
and the direction (use a protractor) of the resultant vector.
Use both head-to-tail and parallelogram methods to add the following two
vectors.
r
Ar = 145 km [45 E of S]
B = 25 km [32 W of N]
r



b) To the resultant vector from question a) add a third displacement vector C
where
r
C = 51 km [80 E of N]

c) Determine the
of the resultant vector rforrthe
r
r following
r magnitude
r r r and direction
expression A B C  D where D = 30 km [54 N of W] and A, B, C are
vectors from question 11 a) and b).

r r
d) determine the magnitude and the direction of A B from question 11 using
Vector
– part 2

 Addition and Subtraction
trigonometry (law of sines and cosines)
r
r
e) determine the magnitude and the direction of A B from question 11 using the

component method.

12. A 100-m race is run on 200-m circumference track. The runners run eastward
at the start and bend south. What is the displacement of the endpoint of the race
from the starting point?
Units and dimensional analysis
13. Determine using dimensional analysis if the following equation is correct:
1
d 2  v it  at 2
2

14. Newton’s law of universal gravitation is represented by
F
GMm
r2
where F is the magnitude of the gravitational force exerted by one object on
another, M and m are the masses of the objects and r is the distance.

a)
b)
what are the SI units of the force?
what are the SI units of the proportionality constant G?
16. Using dimensional analysis find the right expression for the equation in
question 13 and solve for t.
15. A safety inspector at a playground takes measurements to determine the
acceleration of a child undergoing circular motion on a rotating ride. The
inspector uses two common, nonelectric measuring devices.
(a) Based on the units of acceleration, what measuring devices could the
inspector use to take measurements to determine the acceleration?
(b) Name the independent and dependent variables.
Free Body Diagrams, Newton’s Laws
16. A 20-g mass and a 50-g mass are dropped from rest from the same height
above the floor.
(a) Will the masses land simultaneously? If not, which will land first? Explain
your choice.
(b) Draw a free-body diagram showing all the forces acting on the 50-g mass as
it is falling.
(c) What is the weight of the 20-g mass?
(d) Give one example of an action–reaction pair of forces in this situation.
17. The figure below depicts a puck moving on an x-y plane. The dots represent
the location of the puck at equal time intervals of 0.10 s.
(a) What total time elapses between the start and finish of this motion?
(b) Copy the pattern of dots into your notebook, and determine the x-component
of the displacement between each set of dots. What do you conclude about the
motion in the x direction?
(c) Determine the y-component of the displacement between each set of dots.
What do you conclude about the motion in the y direction?
(d) Assuming that the diagram is drawn to the scale 1.0 cm = 5.0 cm, determine
the average velocity between the start and finish of the motion.
18. a) Using free body diagrams show all the forces that are acting 1) on the dog
2) on the sled (assume that the system (sled + dog) is moving on a horizontal
plane).
b) Identify and indicate on your diagram all the action-reaction pairs of forces.
c) Under what condition does the system (sled + dog) move with constant
velocity.
Figure 2
19. Does the force of friction between the sled and the snow in Figure 2. depends
on the area of contact between the surfaces? Explain your answer.