Question

Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25° west of north, and the resultant of these two pulls is 350.0 N directly northward. Find the magnitude of the smaller pull.

A. 149 N
B. 159 N
C. 152 N
D. 144 N

Answer 1

The magnitude of the smaller pull is determined as 149 N (Option A).

How to calculate the magnitude of the smaller pull?

The magnitude of the smaller pull is calculated by applying the following method.

Let the larger force = F₁

the smaller force = F₂

then, F₁ = 2F₂

From the vector diagram, the value of the smaller force (F₂) is calculated by applying Cosine rule as follows.

F₂² = F₁² + 350² - 2(F₁)(350) cos(25)

F₂² = (2F₂)² + 350² - 2(2F₂)(350) cos(25)

F₂² = 4F₂² + 122,500 - 1,268.8F₂

0 = 3F₂² - 1,667.6F₂ + 122,500

We will solve the above quadratic equation using formula method.

a = 3, b = - 1,268.8, c = 122,500

F₂ = 273.8 N or 149.1 N

So the value of the smaller force is 149 N.