Question

Part E Two forces, of magnitude 4N4N and 10N10N, are applied to an object. The relative direction of the forces is unknown. The net force acting on the object __________. Check all that apply.

Answer 1

Answer:

A.) cannot be equal to 5N

Explanation:

Forces are vectors: therefore, when two forces act together on the same object, in order to find the resultant force we must apply the rule of additions for vectors.

Therefore, given two forces $F_1,F_2$, the magnitude of the resultant force can have:

- A minimum value of $|F_1-F_2|$, if the two forces have opposite direction

- A maximum value of $|F_1+F_2|$, if the two forces have same direction

In this problem, the two forces that we have are

$F_1=4 N\\F_2=10 N$

Therefore, the minimum and maximum magnitude of the net force is

$F_{min}=|4-10|=6 N\\F_{max}=|4+10|=14 N$

So the correct statement is

A.) cannot be equal to 5N

Other statements are wrong because:

B.) cannot be equal to 10N --> 10 N is between the interval 6-14 N

C.) cannot be directed the same way as the force of 10N --> the net force has the same direction of the 10 N force, if also the 4N force has the same direction

D.) must be greater than 10N  --> the net force can have up to a magnitude of 14 N