a handbag weighing 162N is carried by the students each holding the handle of the bag next to him. If each handle is inclined at 60° to the vertical, find the force on each students arm
162cos60 and 162sin60
81N and 140.3N
Up forces
To find the force on each student's arm while carrying the handbag, we need to resolve the weight of the handbag into its vertical and horizontal components.
Step 1: Resolve the weight into vertical and horizontal components
The weight of the handbag is 162N. Since each handle is inclined at 60° to the vertical, we need to find the vertical and horizontal components of the weight.
The vertical component (Fv) can be found using the formula: Fv = F × sin(θ), where F is the weight and θ is the incline angle.
Fv = 162N × sin(60°)
Fv = 162N × 0.866
Fv ≈ 140.292N
The horizontal component (Fh) can be found using the formula: Fh = F × cos(θ), where F is the weight and θ is the incline angle.
Fh = 162N × cos(60°)
Fh = 162N × 0.5
Fh = 81N
Step 2: Calculate the force on each student's arm
Since there are two students carrying the handbag, the force on each student's arm is equal to half of the horizontal component (Fh).
Force on each student's arm = Fh / 2
Force on each student's arm = 81N / 2
Force on each student's arm = 40.5N
Therefore, the force on each student's arm is approximately 40.5 Newtons.