Question

part 3:
the way the springs are arranged will affect the effective spring constant (k_eff) of the spring

1. for the given diagram, the mass of the block is 2m

diagram of two springs in parallel attached to a block
which of the following is the correct k_eff?
options:
a) k_eff = k₁ + k₂
b) k_eff = k₁/k₂
c) k_eff = k₁k₂
d) k_eff = (k₁ + k₂)/2

1. for the given diagram, the mass of the block is m. the spring constant of both springs is k.

diagram of two springs in series attached to a block
which of the following is the correct k_eff?
options:
a) k_eff = 2k
b) k_eff = k²
c) k_eff = k/2
d) k_eff = k

Explanation:

Question 1

Step1: Identify Spring Arrangement

The springs are in parallel (both connected to the block and fixed at the same end, so displacement is same for both). For parallel springs, the effective spring constant is the sum of individual constants.

Step2: Recall Parallel Spring Formula

For parallel springs with constants \( k_1 \) and \( k_2 \), \( k_{\text{eff}} = k_1 + k_2 \).

Step1: Identify Spring Arrangement

The springs are in series (one attached to the block, the other between the first spring and the support, so force is same, displacement adds). For series springs with equal constants \( k \), the formula is \( \frac{1}{k_{\text{eff}}} = \frac{1}{k} + \frac{1}{k} \).

Step2: Solve for \( k_{\text{eff}} \)

\( \frac{1}{k_{\text{eff}}} = \frac{2}{k} \), so \( k_{\text{eff}} = \frac{k}{2} \).

Answer:

a. \( k_{\text{eff}} = k_1 + k_2 \)

Question 2