There are two forces acting on a box of golf balls, F1 and F2. The mass of the box is 0.750 kg. When the forces act in the same direction, they cause an acceleration of 0.450 m/s2. When they oppose one another, the box accelerates at 0.240 m/s2 in the direction of F2. (a) What is the magnitude of F1? (b) What is the magnitude of F2?
(a) (1/5 submissions used) N
(b) (1/5 submissions used) N
F1+F2=m(.450)
F1-F2=m(-.240)
add the equations.
To find the magnitudes of F1 and F2, 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.
(a) To find the magnitude of F1, we need to consider the situation where the forces act in the same direction. In this case, the net force is the vector sum of F1 and F2. Using the equation F_net = m * a, we can set up the following equation:
F1 + F2 = m * a
Substituting the given values, we have:
F1 + F2 = 0.750 kg * 0.450 m/s^2
Simplifying, we get:
F1 + F2 = 0.3375 kg m/s^2
To find F1, we need to isolate it in the equation. Subtracting F2 from both sides, we have:
F1 = 0.3375 kg m/s^2 - F2
(b) To find the magnitude of F2, we need to consider the situation where the forces oppose one another. In this case, the net force is the vector difference of F1 and F2. Using the equation F_net = m * a, we can set up the following equation:
F1 - F2 = m * a
Substituting the given values, we have:
F1 - F2 = 0.750 kg * 0.240 m/s^2
Simplifying, we get:
F1 - F2 = 0.18 kg m/s^2
To find F2, we need to isolate it in the equation. Subtracting F1 from both sides, we have:
F2 = -0.18 kg m/s^2 + F1
Now, to find the magnitudes of F1 and F2, we need to substitute the expressions we found for F1 and F2 in the respective equations:
(a) F1 = 0.3375 kg m/s^2 - F2
(b) F2 = -0.18 kg m/s^2 + F1
By solving these two equations simultaneously, we can find the magnitudes of F1 and F2.