**Spring force **(F_{s}) is defined by the hooke’s law. Using the equation of spring force: **F**_{s}** = k Δx**, the value of force exerted by spring on an object can be calculated. (Δx is **+ve** when spring is stretched and Δx is **-ve** when spring is compressed)

Let’s solve some problems based on this equation, so you’ll get a clear idea.

## Spring Force Practice Problems

**Problem 1:** When a block attached to a spring of length 25 cm moves righwards, a spring gets stretched by 50 cm. Calculate the force exerted by spring on a block. (Take the value of spring constant, k = 75 N/m)

Solution:

Given data:

Initial length of a spring, x_{0} = 25 cm = 0.25 m

Final length of a spring, x = 50 cm = 0.5 m

Force exerted by spring on a block, F_{s} = ?

Spring constant, k = 75 N/m

Using the equation of spring force,

F_{s} = k Δx = k × (x – x_{0})

F_{s} = 75 × (0.5 – 0.25)

F_{s} = 75 × 0.25

F_{s} = 18.75 N

Therefore, the force exerted by spring on a block is **-18.75 N**. (left)

**Problem 2:** When a block attached to a spring of length 15 cm moves leftwards, a spring gets compressed by 5 cm. Calculate the force exerted by spring on a block. (Take the value of spring constant, k = 55 N/m)

Solution:

Given data:

Initial length of a spring, x_{0} = 15 cm = 0.15 m

Final length of a spring, x = 5 cm = 0.05 m

Force exerted by spring on a block, F_{s} = ?

Spring constant, k = 55 N/m

Using the equation of spring force,

F_{s} = k Δx = k × (x – x_{0})

F_{s} = 55 × (0.05 – 0.15)

F_{s} = 55 × (-0.01)

F_{s} = -5.5 N

Therefore, the force exerted by spring on a block is **5.5 N**. (right)

**Problem 3:** One spring is resting on the floor. The left end of spring is fixed in the wall and its right end is fixed with a wooden crate. When a wooden crate moves rightwards, a spring gets stretched and the length of spring changes from 0.5 m to 0.65 m. Calculate the force exerted by spring on a wooden crate. (Take the value of spring constant, k = 150 N/m)

Solution:

Given data:

Initial length of a spring, x_{0} = 0.5 m

Final length of a spring, x = 0.65 m

Force exerted by spring on a wooden crate, F_{s} = ?

Spring constant, k = 150 N/m

Using the equation of spring force,

F_{s} = k Δx = k × (x – x_{0})

F_{s} = 150 × (0.65 – 0.5)

F_{s} = 150 × (0.15)

F_{s} = 22.5 N

Therefore, the force exerted by spring on a wooden crate is **-22.5 N**. (left)

**Problem 4:** One spring is resting on the floor. The left end of spring is fixed in the wall and its right end is fixed with a wooden crate. When a wooden crate moves leftwards, a spring gets compressed and the length of spring changes from 0.5 m to 0.2 m. Calculate the force exerted by spring on a wooden crate. (Take the value of spring constant, k = 170 N/m)

Solution:

Given data:

Initial length of a spring, x_{0} = 0.5 m

Final length of a spring, x = 0.2 m

Force exerted by spring on a wooden crate, F_{s} = ?

Spring constant, k = 170 N/m

Using the equation of spring force,

F_{s} = k Δx = k × (x – x_{0})

F_{s} = 170 × (0.2 – 0.5)

F_{s} = 170 × (-0.3)

F_{s} = -51 N

Therefore, the force exerted by spring on a wooden crate is **51 N**. (right)

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**Related:**

- Force Equation
- Normal Force Equation
- Net Force Formula
- Applied Force Formula
- Magnetic Force Equation
- Centripetal Force Equation
- Centrifugal Force Equation
- Tension Force Formula
- Electric Force Equation

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