11.8 CHAPTER 11. VECTORS
(c) Confirm your answers in the previous 2 subquestions with calculations.
- An object of weight W is supported by twocables
attached to the ceiling and wall as shown. Thetensions
in the two cables are T 1 and T 2 respectively. Tension
T 1 = 1200 N. Determine the tension T 2 and weight W
of the object by accurateconstruction and measurement
or by calculation.
T 1
T 2
W
45 ◦
70 ◦
- In a map-work exercise, hikers are requiredto walk from a tree marked A on the map
to another tree marked Bwhich lies 2,0 km due East of A. The hikers thenwalk in a
straight line to a waterfall in position C which has components measured from B of
1,0 km E and 4,0 km N.
(a) Distinguish betweenquantities that are described as being vector and scalar.
(b) Draw a labelled displacement-vector diagram (not necessarily to scale) of the
hikers’ complete journey.
(c) What is the total distance walked by the hikers from their starting point at A to
the waterfall C?
(d) What are the magnitude and bearing, to thenearest degree, of the displacement
of the hikers from their starting point to the waterfall?
- An object X is supported by two strings, A and B, attached
to the ceiling as shownin the sketch. Each of these strings
can withstand a maximum force of 700 N. The weight of X
is increased gradually.
(a) Draw a rough sketchof the triangle of forces,and use
it to explain which string will break first.
(b) Determine the maximum weight of X which can be
supported.
X
A B
30 ◦ 45 ◦
- A rope is tied at two points which are 70cm apart from each other, on the same
horizontal line. The total length of rope is 1 m, and the maximum tension it can
withstand in any part is1000 N. Find the largest mass (m), in kg, that can be carried
at the midpoint of the rope, without breaking the rope. Include a vectordiagram in
your answer.
m
70 cm
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(1.) 00nc (2.) 00nd (3.) 00ne (4.) 00nf (5.) 00ng (6.) 00nh
(7.) 00ni (8.) 00nj (9.) 00nk (10.) 00nm (11.) 00nn (12.) 00np
(13.) 00nq (14.) 00nr (15.) 00ns (16.) 00nt (17.) 00nu
