Question

Two forces and are applied to an object whose mass is 9.31 kg. The larger force is . When both forces point due east, the object's acceleration has a magnitude of 0.626 m/s2. However, when points due east and points due west, the acceleration is 0.340 m/s2, due east. Find (a) the magnitude of and (b) the magnitude of . (a) Number Entry field with correct answer 4.5 Units Entry field with correct answer

Answer 1

the magnitudes of the two forces are 45.N and 1.5 N

Step-by-step explanation:

This in a problem of composition of forces, as the forces are on a single axis, East-West, we can work as a problem of a single dimension, write Newton's second law for each case n

• Two forces to the east

F1 + F2 = m a1

• One force to the east and the other to the west

F1 - F2 = m a2

We see that we have a system of two equations with two unknowns, we proceed to solve it

We add sides equations

F1 + F2 = m a1

F1 - F2 = m a2

2F1 = m (a1 + a2)

F1 = m (a1 + a2) / 2

F1 = 9.31 (0.626 +0.340) / 2

F1 = 4.5 N

We substitute in one of the two equations and find the other force

F1 + F2 = m a1

F2 = m a1 - F1

F2 = 9.31 0.646 - 4.5

F2 = 1.5 N

These are the magnitudes of the two forces 45.N and 1.5 N