Question

Two forces P and Q act on an object of mass 7.00 kg with Q being the larger of the two forces. When both forces are directed to the left, the magnitude of the acceleration of the object is 1.30 m/s2. However, when the force P is directed to the left and the force Q is directed to the right, the object has an acceleration of 0.600 m/s2 to the right. Find the magnitudes of the two forces P and Q in newtons.

Answer 1

P = 2.45 N

Q = 6.65 N

Step-by-step explanation:

According to Newton's 2nd Law:

Unbalanced Force = ma

where,

m = mass = 7 kg

a = acceleration

In the first case when both forces P and Q act on left side:

Unbalanced Force = P + Q

a = 1.3 m/s²

Therefore,

P + Q = (7 kg)(1.3 m/s²)

P + Q = 9.1 N ------------------------- equation 1

Now, in second case when both forces have different directions:

Unbalanced Force = Greater Force - Smaller Force

Unbalanced Force = Q - P

a = 0.6 m/s²

Therefore,

Q - P = (7 kg)(0.6 m/s²)

Q - P = 4.2 N ------------------- equation 2

Adding equation 1 and equation 2, we get:

(Q + P) + (Q - P) = 9.1 N + 4.2 N

2 Q = 13.3 N

Q = 6.65 N

Using this value in equation 2, we get:

6.65 N - P = 4.2 N

P = 2.45 N