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?
F1+F2 = m*a = 0.750 * 0.450 = 0.3375 N.
Fi-F2 = 0.750 * 0.240 = 0.18 N.
Eq1: F1 + F2 = 0.3375
Eq2: F1 - F2 = 0.1800
Sum: 2F1 = 0.5175
F1 = 0.25875 N.
In Eq1, replace F1 with 0.25875
0.25875 + F2 = 0.3375
F2 = 0.3375 - -0.25875 = 0.07875 N.
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.
Let's solve the problem step by step:
(a) To find the magnitude of F1, we need to consider the case where the forces F1 and F2 act in the same direction.
In this case, the net force (F_net) acting on the box can be expressed as:
F_net = F1 + F2
Given that the mass of the box (m) is 0.750 kg and the acceleration (a) is 0.450 m/s^2, we can use Newton's second law to set up the equation:
F_net = m * a
Substituting the given values, we have:
F1 + F2 = (0.750 kg) * (0.450 m/s^2)
Now, we can solve for F1 by rearranging the equation:
F1 = (0.750 kg) * (0.450 m/s^2) - F2
(b) Similarly, to find the magnitude of F2, we need to consider the case where the forces oppose one another.
In this case, the net force (F_net) acting on the box can be expressed as:
F_net = F1 - F2
Given that the mass of the box (m) is 0.750 kg and the acceleration (a) is 0.240 m/s^2, we can use Newton's second law to set up the equation:
F_net = m * a
Substituting the given values, we have:
F1 - F2 = (0.750 kg) * (0.240 m/s^2)
Now, we can solve for F2 by rearranging the equation:
F2 = F1 - (0.750 kg) * (0.240 m/s^2)
Using these equations, we can find the magnitudes of F1 and F2 by substituting the values and solving the equations simultaneously.