Now, three masses (m1 = 3.1 kg, m2 = 9.3 kg and m3 = 6.2) hang from three identical springs in a motionless elevator. The springs all have the same spring constant given above.
Now the elevator is moving downward with a velocity of v = -2.9 m/s but accelerating upward at an acceleration of a = 3.6 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)
What is the magnitude of the net force on the middle mass?
I got 33.48 by using F=ma and that was wrong, so was the negative answer.
please scroll down
https://www.jiskha.com/questions/1775371/Now-three-masses-m1-3-1-kg-m2-9-3-kg-and-m3-6-2-hang-from-three-identical#1777035
To find the magnitude of the net force acting on the middle mass, we need to consider the forces acting on it. In this scenario, there are two forces acting on the middle mass:
1. Gravity force (weight): Given by the equation F_gravity = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Spring force: Given by Hooke's law, F_spring = -k * x, where k is the spring constant and x is the displacement from the equilibrium position. Since the elevator is moving downward with an upward acceleration, the displacement of the middle mass is given by x = -v * t - 0.5 * a * t^2, where v is the velocity and a is the acceleration. The negative sign indicates that the displacement is in the opposite direction of the velocity.
To find the magnitude of the net force on the middle mass, we need to sum up the gravitational force and the spring force:
F_net = F_gravity + F_spring
Let's calculate it step by step:
1. Calculate the gravitational force on the middle mass:
F_gravity = m2 * g = 9.3 kg * 9.8 m/s^2 = 91.14 N
2. Calculate the displacement of the middle mass:
x = -v * t - 0.5 * a * t^2 = -(-2.9 m/s) * t - 0.5 * (3.6 m/s^2) * t^2 = 2.9t - 1.8t^2
3. Calculate the spring force on the middle mass:
F_spring = -k * x = -k * (2.9t - 1.8t^2)
4. Calculate the net force on the middle mass:
F_net = F_gravity + F_spring = 91.14 N - k * (2.9t - 1.8t^2)
Since the problem doesn't provide the value of the spring constant (k), we cannot calculate the exact magnitude of the net force without this information. Therefore, I suggest rechecking the given information or providing the value of the spring constant (k) to determine the correct magnitude of the net force on the middle mass.