Instructions:
• Format: Calculations and drawings must be handwritten, either on paper or digitally.
• Clarity: Organize your work neatly, ensuring it's easy to read and follow.
PROBLEM 1.1 [3 pts]: Perform the following unit conversions using an appropriate prefix:
(a) 200 lb · ft >> N · m
4.448 0.3048
200 lb · ft × ( )×( ) = 271 ·
1 1
(b) 350 lb/ft3 >> kN/m3
350 4.448 1 3
3 3
3 ×( ) × (0.3048 ) = 54977.9 ⁄ = 55.0 ⁄
1
(c) 8 ft/h >> mm/s
8 0.3048 1ℎ
×( ) × (3600 ) = 3.77 × 104 ⁄ = 0.677 ⁄
ℎ 1
PROBLEM 1.2 [4 pts]: Round off the following numbers to three significant figures:
(a) 58 342 m >> 58.3 km
(b) 68.534 s >> 68.5 s
(c) 2553 N >> 2.55 kN
(d) 7555 kg >> 7.56 Mg
PROBLEM 1.3 [3 pts]: Represent each of the following quantities in the correct SI form using
an appropriate prefix:
(a) 0.000431 kg >> 0.431 g
(b) 35.3(103) N >> 35.3 kN
(c) 0.00532 km >> 5.32 m
,PROBLEM 1.4 [5 pts]: Determine the unknown geometrical properties of the following triangles:
sin = ∴ sin 40° =
ℎ 12
= 7.71
cos = ∴ cos 40° =
ℎ 12
= 9.19
(a) = 180 − 90 − 40 = 50.0°
Using the law of sines:
7 8
= ∴ = → = 25.9°
sin sin sin sin 30°
= 180° − 30° − 25.9° → = 124°
8
= ∴ = → = 13.3
sin sin sin 124° sin 30°
(b)
, FORCE VECTORS – PART 1
Instructions:
• Format: Calculations and drawings must be handwritter (paper of your choice).
• Clarity: Organize your work neatly, ensuring it's easy to read and follow.
PROBLEM 2.1: Determine the magnitude of the resultant force acting on the screw eye and its
direction measured clockwise from the x axis. (Use the parallelogram law)
, PROBLEM 2.2: If 𝜃 = 60° and = 450 , determine the magnitude of the resultant force and
its direction, measured counterclockwise from the positive x axis. (Use the parallelogram law)
PROBLEM 2.3: Determine the magnitude of the resultant force and its direction, measured
counterclockwise from the positive x axis. Express the result in cartesian notation.
• Format: Calculations and drawings must be handwritten, either on paper or digitally.
• Clarity: Organize your work neatly, ensuring it's easy to read and follow.
PROBLEM 1.1 [3 pts]: Perform the following unit conversions using an appropriate prefix:
(a) 200 lb · ft >> N · m
4.448 0.3048
200 lb · ft × ( )×( ) = 271 ·
1 1
(b) 350 lb/ft3 >> kN/m3
350 4.448 1 3
3 3
3 ×( ) × (0.3048 ) = 54977.9 ⁄ = 55.0 ⁄
1
(c) 8 ft/h >> mm/s
8 0.3048 1ℎ
×( ) × (3600 ) = 3.77 × 104 ⁄ = 0.677 ⁄
ℎ 1
PROBLEM 1.2 [4 pts]: Round off the following numbers to three significant figures:
(a) 58 342 m >> 58.3 km
(b) 68.534 s >> 68.5 s
(c) 2553 N >> 2.55 kN
(d) 7555 kg >> 7.56 Mg
PROBLEM 1.3 [3 pts]: Represent each of the following quantities in the correct SI form using
an appropriate prefix:
(a) 0.000431 kg >> 0.431 g
(b) 35.3(103) N >> 35.3 kN
(c) 0.00532 km >> 5.32 m
,PROBLEM 1.4 [5 pts]: Determine the unknown geometrical properties of the following triangles:
sin = ∴ sin 40° =
ℎ 12
= 7.71
cos = ∴ cos 40° =
ℎ 12
= 9.19
(a) = 180 − 90 − 40 = 50.0°
Using the law of sines:
7 8
= ∴ = → = 25.9°
sin sin sin sin 30°
= 180° − 30° − 25.9° → = 124°
8
= ∴ = → = 13.3
sin sin sin 124° sin 30°
(b)
, FORCE VECTORS – PART 1
Instructions:
• Format: Calculations and drawings must be handwritter (paper of your choice).
• Clarity: Organize your work neatly, ensuring it's easy to read and follow.
PROBLEM 2.1: Determine the magnitude of the resultant force acting on the screw eye and its
direction measured clockwise from the x axis. (Use the parallelogram law)
, PROBLEM 2.2: If 𝜃 = 60° and = 450 , determine the magnitude of the resultant force and
its direction, measured counterclockwise from the positive x axis. (Use the parallelogram law)
PROBLEM 2.3: Determine the magnitude of the resultant force and its direction, measured
counterclockwise from the positive x axis. Express the result in cartesian notation.
