A vector drawn 8.5 cm long represents a force of 22 N. What force does a vector that is 16.8 cm long, drawn to the same scale, represent? Answer in units of N.
f / 22 = 16.8 / 8.5
To determine the force represented by a vector that is 16.8 cm long, drawn to the same scale, we can use the concept of proportional relationship.
Given:
Length of the first vector = 8.5 cm
Force represented by the first vector = 22 N
We can set up a proportion using the lengths of the vectors and the forces they represent:
(Force of the first vector / Length of the first vector) = (Force of the second vector / Length of the second vector)
Plugging in the given values:
(22 N / 8.5 cm) = (Force of the second vector / 16.8 cm)
To find the force of the second vector, we can solve for it. Rearrange the equation to isolate the force of the second vector:
Force of the second vector = (22 N / 8.5 cm) * 16.8 cm
Calculating this expression:
Force of the second vector = (22 N / 8.5 cm) * 16.8 cm
= 369.882 N
Therefore, a vector that is 16.8 cm long, drawn to the same scale, represents a force of approximately 369.882 N.