Two forces A and B are applied to an object whose mass is 12.3 kg. The larger force is A . When both forces point due east, the object's acceleration has a magnitude of 0.443 m/s2. However, when A points due east and B points due west, the acceleration is 0.280 m/s2, due east. Find (a) the magnitude of A and (b) the magnitude of B.
Fa+Fb = M*a = 12.3 * 0.443 = 5.45 N.
Fa-Fb = 12.3 * 0.280 = 3.44 N.
a. Fa + Fb = 5.45.
Fa - Fb = 3.44.
Sum: 2Fa = 8.89.
Fa = 4.45 N.
b. Fa + Fb = 5.45
4.45 + Fb = 5.45.
Fb = 1.00 N.
To solve this problem, we can use Newton's second law of motion, which states that F = ma, where F is the net force applied to an object, m is the mass of the object, and a is the acceleration of the object.
Let's start by finding the magnitude of force A:
(a) To find the magnitude of force A when both forces point due east, we can use the formula F = ma. Since the object's mass is given as 12.3 kg and the acceleration is given as 0.443 m/s^2, we can write the equation as A - B = ma. Here, B represents the magnitude of force B.
Next, let's find the magnitude of force B:
(b) To find the magnitude of force B when A points due east and B points due west, we use the same formula F = ma. This time, the acceleration is given as 0.280 m/s^2 due east. So the equation becomes A + B = ma.
To solve these two equations simultaneously, we can use the method of substitution. Rearranging the equations, we get:
A - B = 12.3 * 0.443 (Equation 1)
A + B = 12.3 * 0.280 (Equation 2)
Adding Equation 1 and Equation 2, we eliminate B:
2A = (12.3 * 0.443) + (12.3 * 0.280)
2A = 5.4441 + 3.444
Dividing both sides of the equation by 2, we find:
A = (5.4441 + 3.444) / 2
A = 8.8881 / 2
A = 4.44405 N
Now that we have found the magnitude of force A, we can substitute this value back into Equation 1 to find the magnitude of force B:
4.44405 - B = 12.3 * 0.443
- B = 12.3 * 0.443 - 4.44405
B = (12.3 * 0.443) - 4.44405
B = 5.4441 - 4.44405
B = 1.00005 N
Therefore, the magnitude of force A is approximately 4.444 N, and the magnitude of force B is approximately 1.000 N.