A light spring of constant k = 170 N/m rests vertically on the bottom of a large beaker of water. A 5.70 kg block of wood (density = 650 kg/m3) is connected to the spring and the mass-spring system is allowed to come to static equilibrium. What is the elongation, ÄL, of the spring?
To find the elongation of the spring, we need to consider the balance of forces acting on the system. Since the system is in static equilibrium, the upward force exerted by the spring must be equal to the downward force exerted by the weight of the block.
Let's break down the problem step by step:
1. Calculate the weight of the block:
The weight of the block can be calculated using the formula: weight = mass × gravitational acceleration.
Given the density (ρ) of the block as 650 kg/m^3 and the mass (m) of the block as 5.70 kg, we can find the volume (V) of the block using the formula: V = m/ρ.
Using the value of V, we can now calculate the weight of the block using the formula above.
2. Calculate the elongation of the spring:
Since the system is in equilibrium, the force exerted by the spring must be equal to the weight of the block. The force exerted by the spring, according to Hooke's Law, is given by the formula: F = k × ΔL, where F is the force exerted by the spring, k is the spring constant, and ΔL is the elongation of the spring.
Therefore, we can rearrange the formula to find the elongation of the spring: ΔL = F/k.
Substituting the weight of the block as the force exerted by the spring, we can find the elongation of the spring.
Let's calculate it step by step:
1. Calculate the weight of the block:
Weight = mass × gravitational acceleration
Weight = 5.70 kg × 9.8 m/s^2
2. Calculate the volume of the block:
V = m/ρ
V = 5.70 kg / 650 kg/m^3
3. Calculate the weight of the block in water:
Weight = Density of water × Volume × gravitational acceleration
Density of water is approximately 1000 kg/m^3.
4. Calculate the net force exerted by the spring:
Force exerted by the spring = Weight of the block in water
5. Calculate the elongation of the spring:
ΔL = F/k, where F is the force exerted by the spring and k is the spring constant.
Substituting the values, you'll be able to find the elongation of the spring.