A handbag containing some load weighing 162N is carried by two students each holding the handle of the bag next to him. If each handle is pulled \( 60^{\circ} \) to the vertical, find the force on each student's arm
A
81N
B
121N
C
162N
D
324N
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Weight of handbag(W) = 162N acting vertically downward
Angle of pull (\(\theta\)) = 60º to the vertical
Since the handbag is in equilibrium, the total vertical force must equal the weight of the handbag.
Let F be the force exerted by each student on the handle. The vertical component of the force from each student is given by:
Fv = F cos 60º but there are two students
2Fcos60º = 162
2F(0.5) = 162 ( cos60º = 0.5)
F = 162 ( since 2 x 0.5 = 1)
Therefore, the force exerted by each student on the handbag is: 162N
Source: Official Exam / Past Question Archive