ASSIGNMENT
2
MARLON DZEPASI C19140258E
MADZIWA TIMOTHY C20143127O
GROUP 4
QSN)The handcart has a mass of 200 kg and center of mass at G.
Determine the largest magnitude of force P that can be applied to the
handle so that the wheels at A or B continue to maintain contact with
the ground. Neglect the mass of the wheels.
P
Mg
0,3m
FBD
𝑎𝐺
200(9,81)N
600
0,3m 0,2m 0,4m
𝑁𝐴
𝑁𝐵
+ ∑Fx = m(𝑎𝐺 )x
PCos60= 200 𝑎𝐺
P=
200
𝑎
𝐶𝑜𝑠600 𝐺
P = 400𝑎𝐺
+
∑ Fy = m(𝑎𝐺 )y
𝑁𝐴 + 𝑁𝐵 - 200(9,81) - PSin600 = m(𝑎𝐺 )y
𝑁𝐴 + 𝑁𝐵 - 1962 - 0,866P = m(𝑎𝐺 )y
MOMENT OF G
−𝐴 (0,3) + 𝑁𝐵 (0,2) + PCos600 (0,3) - PSin600 (0,6) = 0
-0,3𝑁𝐴 + 0,2𝑁𝐵 - 0,3696P = 0
+
∑ Fy = 0
𝑁𝐴 + 𝑁𝐵 - 1962 - 0,866P = 0
AT Pmax 𝑁𝐴 = 0
• 𝑁𝐵 - 0,866P = 1962 ......... (1)
• 0,2𝑁𝐵 - 0,3696P = 0 ..........(2)
• 𝑁𝐵 = 1,848P
•
0,982
0,982
=
1962
0,982
• P = 1997,96N (Ans)
• which is also 2KN
• 𝑁𝐵 = 1,828(1997,96)
•
= 3692N
• 3692 - 1962 - 0,866(1997,96) = 200(𝑎𝐺 )y
• (𝑎𝐺 )y = -0,0011668 𝑚 𝑠 2
(𝑎𝐺 )x =
1997,96
400
= 4,9949𝑚 𝑠 2
so a = (4,9946)2 + (−0,0011668)2
= 4,9946𝑚 𝑠 2