Answer:
0.00256 m
Explanation:
For this case, we should use the Hook Law for a spring:
F= -Kx , the negative sign indicates that the force that tries to “restore” the original status of the spring, and is against the force that causes the spring´s displacement
This is, the force F required to stretch an elastic object (for example, a metal spring), is directly proportional the extension “x” of the spring
“x” can be the extension or compression of the spring, and “K” is a constant (in units of N/m)
We also know that, according to Newton´s Law:
F=m*a
m= mass
a= acceleration
Then:
m*a= -Kx
Finally, the spring has an original length of L₀, so:
- If the spring is compressed, the final strength will be: L = L₀ – x
- If the spring is extended, the final strength will be: L = L₀ + x
According to the statement:
K = 802 N/m
a = 0.41 m/s2
m = 5 Kg
Then:
x =- (m*a)/K = (5x0.41)/802 = 0.00256 m (we do not consider the negative sign, due to above explanation: it only indicates that the restoration force is always against the force imposed on the spring
)
So, if the spring has an original length of L₀, when the elevator is accelerating upwards, the spring will stretch from L₀ to (L₀ – 0.00256) m
