Question

two men are pushing a car with a force of 16 pounds. if the car weighs 2750 pounds, what is the total force being applied to the car? round your answer to four decimals.

Explanation:

Step1: Analyze the forces

The weight of the car acts vertically downwards ($F_{weight} = 2750$ pounds) and the force applied by the men acts horizontally ($F_{push}=16$ pounds). Since these two forces are perpendicular to each other, we use the Pythagorean theorem for vectors. The formula for the magnitude of the resultant force $F$ when two perpendicular forces $F_1$ and $F_2$ are applied is $F=\sqrt{F_1^{2}+F_2^{2}}$. Here, $F_1 = 2750$ and $F_2=16$.

Step2: Calculate the resultant force

Substitute the values into the formula:
$$F=\sqrt{2750^{2}+16^{2}}=\sqrt{7562500 + 256}=\sqrt{7562756}$$
$$F = 2750.0465$$

Answer:

$2750.0465$