MATHEMATICS

Mathematics of Force and Motion

Mathematics of Force and Motion

Question No. 1

At the end of the week number

Plant Height (cm)

1

0.7

2

2.1

3

3.4

4

4.7

5

6.1

6

7.5

7

8.8

8

10.2

9

11.5

10

12.9

Total

67.9

a) What is the plant's average weekly growth, for each of the 10 weeks?

Average weekly growth of plant

=

67.9

=

6.79

10

b) Determine an equation that gives the height of the plant for any given week.

X 2

=

X 1

+

1.4

X 2

=

0.7

+

1.4

2.1

=

0.7

+

1.4

c) Graph this equation.

From the above graphical representation, it can be observed that at the end of week 1, the height of the plant was 0.7 which increased by 1.4 from week 1 to week 2; consequently, the height of plant in week 2 was 2.1.

d) If the plant were to continue growing at the same rate then, what should we expect the plant's height to be after 17 weeks?

If the plant keeps on growing at the same rate that is 1.4, then the height of plant after the 17 weeks would be;

At the end of the week number

Plant Height (cm)

1

0.7

2

2.1

3

3.5

4

4.9

5

6.3

6

7.7

7

9.1

8

10.5

9

11.9

10

13.3

11

14.7

12

16.1

13

17.5

14

18.9

15

20.3

16

21.7

17

23.1

e) If the plant were to continue growing at the same rate then, during which week should the height of the plant reach 35 cm?

If the plant keeps on growing at the same rate that is 1.4, then the height of plant during 26th week will be 35 cm.

At the end of the week number

Plant Height (cm)

18

24.5

19

25.9

20

27.3

21

28.7

22

30.1

23

31.5

24

32.9

25

34.3

26

35.7

Question No. 2

If both Steve and Bill exert same force that is 600 N then the total force they exert on the barrage will be zero as the exerted total force balances the total force on the barrage because the effects of Steve and Bill cancel each other out and do not cause a change in the barrage motion.

Question No. 3

The stress in the string is the tension in the string divided by its cross section area.

T = 37 + 53 = 90

It depends what is meant by the total force of cable in the case. The tension in the string (T) has a vertical component which must precisely balance the downwards force of the weight of the cable. Therefore, the total downward force due to the tension equals to the weight of cable;

W = mg

The angle theta is determined by how much the centre of the string sags.

The vertical component for the cable of the tension is T cos theta + T cos theta.

Magnitude of the force = 37 * 0.798 + 53 * 0.601 = 29.526 + 31.853 = 61.379

Question No. 4

a)

1/ 16 = (0.0625 * 1000 kg) = 62.5 ...