Two forces and are applied to an object whose mass is 5.75 kg. The larger force is . When both forces point due east, the object's acceleration has a magnitude of 0.979 m/s2. However, when points due east and points due west, the acceleration is 0.639 m/s2, due east. Find (a) the magnitude of and (b) the magnitude of .
Find?.
F1+F2= M*a.
Eq1: F1+F2 = 5.75 * 0.979 = 5.63 N.
F1-F2 = M*a.
Eq2: F1-F2 = 5.75*0.639 = 3.67 N.
F1+F2 = 5.63
F1-F2 = 3.67
Sum: 2F1 = 9.30, F1 = 4.65 N.
F1-F2 = 3.67, 4.65-F2 = 3.67, F2 = 0.98 N.
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's start by setting up the equations for the two scenarios:
1. When both forces point due east:
From the information given, the larger force (F1) is in the same direction as the object's acceleration (due east), and therefore:
F1 - F2 = m * a1 ----> Equation 1
2. When F2 points due east and F1 points due west:
In this scenario, the forces have opposite directions. Since acceleration is in the direction of F1, we can write:
F1 + F2 = m * a2 ----> Equation 2
Now, let's solve these equations to find the magnitudes of F1 and F2:
(a) Magnitude of F1:
From Equation 1, we have:
F1 - F2 = m * a1
Substituting the given values:
F1 - F2 = (5.75 kg) * (0.979 m/s^2)
Simplifying the equation:
F1 - F2 = 5.62225 N ----> Equation 3
(b) Magnitude of F2:
From Equation 2, we have:
F1 + F2 = m * a2
Substituting the given values:
F1 + F2 = (5.75 kg) * (0.639 m/s^2)
Simplifying the equation:
F1 + F2 = 3.67125 N ----> Equation 4
Now, we can solve the system of equations (Equation 3 and Equation 4) to find the magnitudes of F1 and F2:
Adding Equation 3 and Equation 4:
(F1 - F2) + (F1 + F2) = 5.62225 N + 3.67125 N
Simplifying the equation:
2F1 = 9.2935 N
Dividing by 2:
F1 = 4.64675 N
Substituting the value of F1 into Equation 3:
4.64675 N - F2 = 5.62225 N
Solving for F2:
F2 = 4.64675 N - 5.62225 N
F2 = -0.9755 N
Since magnitude cannot be negative, we take the absolute value:
|F2| = |-0.9755 N| = 0.9755 N
Therefore, the magnitude of F1 is 4.64675 N and the magnitude of F2 is 0.9755 N.