Question

Two forces and are applied to an object whose mass is 8.93 kg. The larger force is . When both forces point due east, the object's acceleration has a magnitude of 0.919 m/s2. However, when points due east and points due west, the acceleration is 0.693 m/s2, due east. Find (a) the magnitude of and (b) the magnitude of .

Answer 1

Answer:

(a) F1 = 7.19N

(b) F2 = 1.01N

Explanation:

You have the following two forces exerted to an object:

F1: larger force

F2: weaker force

When the forces are in the same direction, to the east, the acceleration of the object is 0.919 m/s^2.

You use the Newton second law to write the following equation:

$F_1+F_2=ma$           (1)

m: mass of the object = 8.93 kg

When the two forces are in opposite direction, one to the east and the other one to the west, you have the following equation (2):

$F_1-F_2=ma'$               (2)

a': acceleration = 0.693 m/s^2

Then, with both equations (1) and (2) you have a 2x2 systems of equation.

You can find the values of F1 and F2 by solving the 2x2 system.

First, you sum equation (1) and (2):

$F_1+F_1+F_2-F_2=ma+ma'\\\\2F_1=m(a+a')$ (3)

You solve the equation (3) for F1:

$F_1=\frac{m(a+a')}{2}=\frac{(8.93kg)(0.919m/s^2+0.693m/s^2)}{2}=7.19N$

Next, you can replace the value of F1 into the equation (1) and you can obtain the value of F2:

$F_2=ma-F_1\\\\F_2=(8.93kg)(0.919m/s^2)-7.19N=1.01N$

Finally, you have:

(a) The values of the larger force is 7.19N

(b) The values of the weaker force is 1.01N