Question

Two forces P and Q act on an object of mass 15.0 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 1.50 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 0.700 m/s² to the right. Find the magnitudes of the two forces P and Q in newtons.

Answer 1

Answer:

P=6.25N  and Q=16.25N

Explanation:

In order to solve this problem we must first draw a free body diagram for both situation, (see attached picture).

Now, we need to analyze the two free body diagrams. So let's analyze the first diagram. Since the body is accelerated, then the sum of forces is equal to mass times acceleration, so we get:

$\Sigma F=ma$

We can assume there will be only the two mentioned forces P and Q, so

the sum of forces will be:

P+Q=ma

$P+Q=(15kg)(1.50m/s^{2})$

P+Q=22.5N

We can do the same analysis for the second free body diagram:

$\Sigma F=ma$

$Q-P=(15kg)(0.7m/s^{2})$

Q-P=10.5N

so now we have a system of equations we can solve by elimination:

Q+P=22.5N

Q-P=10.5N

Now, we can add the two equations together so the P force is eliminated, so we get:

2Q=32.5N

now we can solve for Q:

$Q=\frac{32.5N}{2}$

so

Q=16.25N

Now we can use any of the equations to find P.

Q+P=22.5N

P=22.5N-Q

when substituting for Q we get:

P=22.5N-16.25N

so

P=6.25N