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.) the masses hang in series with one another m3 is on the bottom and m1 is on the top
What is the distance the lower spring is extended from its unstretched length?
somebody please help me
See my comment below. I wonder if they mean net SPRING force ignoring gravity. 208 up - 83.1 down
if I wanted to find the lower spring extended from it's unstretched length, what is a formula that I could use? I found that the distance the middle spring is stretched from its equilibrium length is 44.9cm, would I have to use this as well?
You only need the force in that one spring 83.1 N = k * stretch
HOWEVER if you want the change in position from the ceiling
you must do stretch 1 + stretch 2 + stretch 3
Did they ask for the total distance or just the change in length of that spring?
they weren't very specific with that, the exact wording is the question I posted above
To find the distance the lower spring is extended from its unstretched length, we need to consider the forces acting on it.
First, let's determine the total force acting on the lower spring. The force is the sum of the gravitational force and the spring force:
F_total = F_gravity + F_spring
1. Gravitational Force:
The gravitational force acting on the lower mass (m3) is given by the equation:
F_gravity = m3 * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 6.2 kg * 9.8 m/s^2
F_gravity = 60.76 N
2. Spring Force:
The spring force can be calculated using Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position:
F_spring = k * x
where k is the spring constant and x is the displacement from the equilibrium position.
Since the three masses are in series, they all experience the same displacement x. Therefore, the spring force for the lower spring is:
F_spring = k * x
Now, let's calculate the spring force. You mentioned that the spring constant is given, but unfortunately, it's not provided in the question. Could you provide the value of the spring constant so we can proceed with the calculation?