College

A force of 350 pounds is resolved into component forces. If it makes an angle of 67° with the horizontal, find the larger component.

A. 322 lb
B. 235 lb
C. 137 lb
D. 380 lb

Answer :

Answer: [tex]322\ lb[/tex]

Step-by-step explanation:

Given

The magnitude of the force [tex]F=350\ \text{Pounds}[/tex]

The force makes an angle of [tex]67^{\circ}[/tex] with the horizontal

So, the components of the force are

[tex]\Rightarrow F\cos 67^{\circ}, F\sin 67^{\circ}\\\Rightarrow F\cos 67^{\circ}=350\cos 67^{\circ}\\\quad \quad =136.75\ lb\\\text{Similarly, }\\\Rightarrow F\sin 67^{\circ}=350\sin 67^{\circ}\\=322.17\ lb[/tex]

The larger among the two is [tex]F\sin 67^{\circ}[/tex] i.e. [tex]322\ lb[/tex]

The larger component is approximately 322 pounds .

Resolving a Force into Components

To find the larger component of a force of 350 pounds that makes an angle of 67° with the horizontal, we need to resolve this force into its horizontal and vertical components using trigonometric functions.

  1. Calculate the horizontal component (Fₓ):
    Fₓ = F x cos(θ)
    Fₓ = 350 x cos(67°)
    Fₓ ≈ 350 x 0.3907 ≈ 136.745 pounds
  2. Calculate the vertical component (Fy):
    Fy = F x sin(θ)
    Fy = 350 x sin(67°)
    Fy ≈ 350 x 0.9210 ≈ 322.35 pounds

Since the vertical component is larger, the larger component is approximately 322 pounds.