HWA CHONG INSTITUTION

HWA CHONG INSTITUTION

Secondary 3 Physics

Scalars and vectors

AnswerClass Practice1A barge is pulled at a steady speed through still water by two horizontal cables as shown in the plan view below. By means of a vector diagram, determine the magnitude and direction of the resultant force exerted on the barge by the cables.

[3]

(b) By means of vector resolution, predict where it is possible for the barge to move

horizontally forward, given that the angle between the two cables can be adjusted.

Show your workings and calculate the angle, if necessary.

[2]

2

A motor

boat travels due north at a steady speed of 3.0 m/s through calm water in which there is no current. The boat then enters an area of water in which a steady current flows at 2.0 m/s in a south-west direction as shown in the above figure. Both the engine power and the course setting remain unchanged.

(a) In the space below, draw a vector diagram showing the velocity of the boat and the

velocity of the current. Use a vector diagram to find

(i) the magnitude of the resultant velocity of the boat;

[2](ii) the angle between due North and the direction of the travel of the boat[2]

(b) Calculate the distance the boat now travels in 5.0 min.

[1]

distance = 2.1 x 5 x 60

= 630 m3A mass of weight 14.0 N hanging on the end of a string is pulled sideways so that the string makes an angle of 30o with the vertical as shown in the diagram.

In this position, the tension in the string is 16.0 N. By means of a vector diagram, determine the resultant of the tension in the string and the weight of the mass.

Show clearly on your diagram the direction in which the resultant acts and record its magnitude.

[3]

Assignment Questions

1A boat heads directly across a river, that is 40 m wide, at 8.0 ms-1. The current is flowing at 3.0 ms-1.

(a) Using a vector diagram, determine the resultant speed of the boat.[3]

(b) How long does it take the boat to cross the river?

[1]

Time taken = distance / time

= 40/8

= 5 s

(c) How far downstream is the boat when it reaches the other side?[1]

distance downstream = 5 x 3

= 15 m

2A microphone of mass 500 g hangs from the end of a long wire fixed to the ceiling. A horizontal string attached to the microphone exerts a force that keeps the wire at an angle of 20o to the vertical.

(a)Show the forces acting on the microphone using a free-body diagram . [1]

3A student investigating balanced forces uses the apparatus shown in the figure below. The student notices that for a certain angle ( formed (i.e. the angle the upper part of the thread makes with the vertical), the reading on the spring balance is 22 N.

By drawing a vector diagram to scale, determine

(i) the tension on the upper part of the thread, and [2]

(ii) the angle (.

[2] Scale 1.0 cm : 2.0 N

Questions from Textbook College Physics, Young and Geller4.Pg 26, Q46

[4](Note: only use vector resolution to calculate the answer. No need to draw vector diagram.)

5.Pg 26, Q48

[4](Note: only use vector resolution to calculate the answer. No need to draw vector diagram.)

To find the resultant pull of these three forces,

Step 1: Find resultant of force A and B.

R2 = 802 + 1002

R = 128 N

Step 2: Find resultant of force R and C.Rfinal2 = 1282 + 402 - 2(128)(40) cos 16oRfinal = 90 N

Anticlockwise angle from the x-axis = 30 + 39 + 7

= 76oMagnitude of Rfinal is 90N6. Pg 27, Q62

[4](Note: only use vector resolution to calculate the answer. No need to draw vector diagram.)

Step 1: Find the resultant of the first two displacement vectors

R12 = 2.002 + 3.502 2(2.00) (3.50) cos 135oR1 = 5.11 km

Step 2: Find the displacement of the third leg.R12 = 5.112 + 5.802 2(5.11) (5.80) cos 29oR1 =2.81 km

Answer:Magnitude of displacement = 2.81 km

Direction = 90 (180 29 90)=29o East of North7. Pg 28, Q65

[4](Note: only use vector resolution to calculate the answer. No need to draw vector diagram.)

R12 = 2322 + 132.52 2(232) (132.5) cos 43oR1 =163 N

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