# Spring Force Equation | Problems

Spring force (Fs) is defined by the hooke’s law. Using the equation of spring force: Fs = 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, x0 = 25 cm = 0.25 m
Final length of a spring, x = 50 cm = 0.5 m
Force exerted by spring on a block, Fs = ?
Spring constant, k = 75 N/m

Using the equation of spring force,
Fs = k Δx = k × (x – x0)
Fs = 75 × (0.5 – 0.25)
Fs = 75 × 0.25
Fs = 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, x0 = 15 cm = 0.15 m
Final length of a spring, x = 5 cm = 0.05 m
Force exerted by spring on a block, Fs = ?
Spring constant, k = 55 N/m

Using the equation of spring force,
Fs = k Δx = k × (x – x0)
Fs = 55 × (0.05 – 0.15)
Fs = 55 × (-0.01)
Fs = -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, x0 = 0.5 m
Final length of a spring, x = 0.65 m
Force exerted by spring on a wooden crate, Fs = ?
Spring constant, k = 150 N/m

Using the equation of spring force,
Fs = k Δx = k × (x – x0)
Fs = 150 × (0.65 – 0.5)
Fs = 150 × (0.15)
Fs = 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, x0 = 0.5 m
Final length of a spring, x = 0.2 m
Force exerted by spring on a wooden crate, Fs = ?
Spring constant, k = 170 N/m

Using the equation of spring force,
Fs = k Δx = k × (x – x0)
Fs = 170 × (0.2 – 0.5)
Fs = 170 × (-0.3)
Fs = -51 N

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

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