Question

Two forces Fa and Fb are applied to an object whose mass is 5.42 kg. slader The larger force is Fa. When both forces point due east, the object's acceleration has a magnitude of 0.651 m/s2. However, when Fa points due east and Fb points due west, the acceleration is 0.427 m/s2, due east. Find (a) the magnitude of Fa and (b) the magnitude of Fb.

Answer 1

Fa = 2.92N

Fb = 0.61N

Step-by-step explanation:

According to the Newton's second law,

Force = mass × acceleration

Given two forces Fa and Fb applied on an object,

∑F = ma

If both forces points due east (+x direction)

∑F = Fa+Fb = ma

Fa+Fb = 5.42kg(0.651 m/s²)

Fa+Fb = 3.53... (1)

If Fa points due east (+x drn) and Fb points due west (-ve x direction)

∑F = Fa-Fb = 5.42(0.427)

∑F = Fa-Fb = 2.31... (2)

Solving equation 1 and 2 simultaneously to get the magnitude of the force Fa and Fb

Fa+Fb = 3.53... (1)

Fa-Fb = 2.31... (2)

Adding both equation:

2Fa = 3.53+2.31

2Fa = 5.84

Fa = 5.84/2

Fa = 2.92N

Substituting Fa = 2.92N into equation 2

Fa - Fb = 2.31

2.92 - Fb = 2.31

-Fb = 2.31 - 2.92

-Fb = -0.61

Fb = 0.61N

Answer 2

a)Fa=2.98 N

b)Fb=0.53 N

Step-by-step explanation:

Given that

m= 5.42 kg

When force are acting in east direction:

So from second law of Newton's

Given that Fa is greater than Fb and acceleration is 0.651
`m/s^2`.

Fa+Fb= m a

Fa+ Fb =5.42 x 0.651

Fa+ Fb =3.52 -------------1

Now when both acting in apposite direction

Given that Fa is greater than Fb and acceleration is 0.427
`m/s^2`.

Fa-Fb= m a

Fa- Fb =5.42 x 0.427

Fa- Fb =2.44 -------------2

Now from equation 1 and 2

Add both equations

2 Fa = 5.96

Fa=2.98 N

From equation 1

Fb =3.52 -Fa

Fb=0.53 N