Answer to Question #203968 in Physics for Rethabile

Question

25. A partly full paint can has 2.75 liters of paint left in it. What is volume of the paint in cubic centimeters? (3)

A) 2.75 x 10-3 cm3 C) 275 x 10-3 cm3 E) 27.5 x 103 cm3

B) 2.75 cm3 D) 2.75 x 103 cm3 

26. Calculate the resultant of the four forces working on an object:

25 N 20° W of N

60 N 18° S of W

45 N W

35 N 49° E of N

Use the perpendicular component method. Express the answer in unit vector notation.  (6)

Answer 1

25. 1 L is 1000 mL, 1 mL is 1 cm³, so, 2.75 L is 2750 cm³, or 2.75·10³ cm³

26. Find the components of each force assuming E is +x and N is +y:

$$F_{1x}=-25\text{sin}20°=-8.55\text N.\\ F_{2x}=-60\text{cos}18°=-57.1\text N.\\ F_{3x}=45\text{sin}45°=31.8\text N.\\ F_{4x}=35\text{sin}49°=26.4\text N.\\ \\\space\\ F_{1y}=25\text{cos}20°=23.5\text N.\\ F_{2y}=-60\text{sin}18°=-18.5\text N.\\ F_{3y}=45\text{cos}45°=31.8\text N.\\ F_{4y}=35\text{cos}49°=23\text N.\\$$

The resultant:

$$F_xi+F_yj=(F_{1x}+F_{2x}+F_{3x}+F_{4x})i+\\+(F_{1y}+F_{2y}+F_{3y}+F_{4y})j=\\ =-[7.45i+59.8j]\text{N}.$$