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. I might be using the wrong formula, how would I solve this and how would that look like?
What is the distance the lower spring is extended from its unstretched length?
this is another one I had trouble with, how would I go about doing this one?
first, calcuate the force on each spring due to motion: F=m(g+a)
Next, calculte how far each spring is extended to those individual forces.
x=forceonspring/k
is this for the distance or the magnitude?
Look the "net" force on a rigid body is its mass times its acceleration, like period.
for spring extension I need to know your geometry, series or parallel. Which is the top mass if in series?
To solve this problem, we need to consider the forces acting on the middle mass (m2) in the moving elevator.
First, let's find the individual forces acting on m2. There are two main forces at play: the force due to gravity (weight) and the force exerted by the spring.
1. Weight force (mg):
The weight force is given by the formula F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the weight force acting on m2 is F1 = m2 * g.
2. Spring force (kx):
The spring force is given by Hooke's Law, which states that the force exerted by the spring is directly proportional to the displacement from its equilibrium position. The formula is F = kx, where k is the spring constant and x is the displacement from the equilibrium position. Since the elevator is moving, we need to consider the displacement caused by the motion of the elevator. In this case, the spring force acting on m2 is F2 = k * x.
Now, let's determine the displacement caused by the motion of the elevator. The acceleration of the elevator provides an additional force, which can create an elongation or compression in the spring.
The net force acting on m2 is the vector sum of the weight force and the spring force. Since the elevator is moving downward, the weight force and the spring force will have opposite directions.
Net force (Fnet) = F1 - F2 (because they act in opposite directions)
To find the magnitudes of F1 and F2:
F1 = m2 * g
F2 = k * x
To find the displacement x, we can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Rearranging the equation, we have:
s = (v^2 - u^2) / (2a)
Given:
m2 = 9.3 kg
g = 9.8 m/s^2
k = spring constant (not provided)
v = -2.9 m/s (velocity of the elevator)
a = 3.6 m/s^2 (acceleration of the elevator)
To calculate the spring displacement x, we need the spring constant (k). Since it is not provided, we cannot calculate the exact value of the net force without this information.
Once the spring constant (k) is given, you can substitute the values into the formulas and find the magnitude of the net force on the middle mass (Fnet = F1 - F2).