Calculate the magnitude of the resultant force using

Question

Task 1:

1. Convert the following into degrees and minutes:

- 3Π/8 rads

- 1.26Π rads

2. Convert the following into radians

- 152° 15'
- 17° 56' 22"

3. on the circle below calculate:

a. the length of the major and minor arc and

b. the area of the major and minor sector

When r = 2.5cm and θ = Π/4 radians

c. For the following triangle produce a table stating the values of the sine, cosine and tangent of angles α and θ.

d. Determine the value of x in each of the following right angled triangles

Task 2 :

On a graph plot the following waveforms over a complete cycle:
- Y = 2sin (θ + 30)
- Y = 4Cos 3θ
- Y = 3Tan (θ/2)

Graph paper is available from www.papersnake.com

Task 3 :

1. A crank mechanism of a petrol engine is shown below. The arm OA is 10.0cm long and rotates clockwise about point central point O. The connecting rod AB is 40.0cm long and end B can only move horizontally along length OB.

In its starting position determine the angle B giving your answer in degrees and minutes

2. The diagram below shows two forces acting on object O. Calculate the magnitude of the resultant force using trigonometric methods where F₁ = 7N, F₂ = 4N and θ = 30°

To calculate the Resultant Force (FR)

FR = F₁ + F₂

3. A gear system is being designed where a small 30mm diameter cog is to be fitted between a 70mm diameter driving gear and a 90mm driven gear as shown below. Determine the value of the angle θ between the centre lines.

Calculate the volumes and surface reas of the following solids:

Solid 1: A cone with a radius of 5cm a nd a height of 12cm

Solid 2: The following solid prism

Solid 3: The following wooden block where r = 8cm

Solid 4: the following engineered block

Reasoned calculation (showing full working out) for each of the questions. Your answers should be given to 2 d.p.s with the correct units stated.