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?
F2 + F1 = .450 (.750)
F2 - F1 = .240 (.750)
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2 F2 = .690(.750)
etc
To find the magnitude 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:
When the forces F1 and F2 act in the same direction, the resulting acceleration is 0.450 m/s². So, the net force, F_net, can be calculated as follows:
F_net = m * a
F_net = 0.750 kg * 0.450 m/s²
F_net = 0.338 N
Since we know that the acceleration is caused by both F1 and F2, and we want to find the magnitude of F1, we can set up the following equation:
F_net = F1 + F2
Plugging in the value of F_net, we get:
0.338 N = F1 + F2
(b) To find the magnitude of F2:
When the forces F1 and F2 oppose each other, the resulting acceleration is 0.240 m/s² in the direction of F2. Since the acceleration is in the direction of F2 in this case, we can set up the following equation:
F_net = F2 - F1
Plugging in the known values, we get:
0.338 N = F2 - F1 (equation 1)
0.240 N = F2 - F1 (equation 2)
To solve the system of equations (equations 1 and 2), we can subtract equation 2 from equation 1:
0.338 N - 0.240 N = F2 - F2 + F1
0.098 N = F1
Therefore, the magnitude of F1 is 0.098 N.
To find the magnitude of F2, we can substitute the value of F1 into equation 1:
0.338 N = F2 - 0.098 N
F2 = 0.338 N + 0.098 N
So, the magnitude of F2 is 0.436 N.
In summary:
(a) The magnitude of F1 is 0.098 N.
(b) The magnitude of F2 is 0.436 N.