How Much Work Is Done In Stretching A Spring? (Perfect answer)

  • Solution: The work done in stretching or compressing a spring is proportional to the square of the displacement. If we double the displacement, we do 4 times as much work. It takes 16 J to stretch the spring 20 cm from its unstretched length, so it takes 12 J to stretch it from 10 cm to 20 cm.

How do you calculate work done in stretching a spring?

Let the spring be stretched through a small distance d x dx dx. Then work done in stretching the spring through a distance d x dx dx is d W = F d x, dW=Fdx, dW=Fdx, where F is the force applied to stretch the spring.

What is the work done in stretching the spring?

Elastic potential energy is Potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched.

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What is the formula of work done for stretching?

In stretching a wire work is done against internal restoring forces. This work is stored as elastic potential energy or strain energy. If a force F acts along the length L of the wire or cross section A and stretches it by x then: Young′sModulus(Y)=StressStrain=F/Ax/L=FLAx⇒F=YALx.

How do you calculate work done?

Work can be calculated with the equation: Work = Force × Distance. The SI unit for work is the joule (J), or Newton • meter (N • m). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.

How much work is done in stretching a spring of spring constant k from its unstretched?

When a spring with spring constant k is stretched by distance L from its unstretched length L by an external force acting parallel to the string (figure a), the work done by the external force is W=(1/2)kL2. This work equals the potential energy of the stretched spring.

What is the work done by spring?

Work is equal to force times distance, w=fd. For a spring, f=-kx. So a stretched out or compressed spring will exert more work when x is higher.

Can work done by spring force be positive?

Total work done by spring force may be positive, negative or zero. though we know that the spring force is always directed towards mean position and the spring force is always negative.

How do you calculate spring energy?

Energy stored in a spring

  1. Work is done when a spring is extended or compressed. Elastic potential energy is stored in the spring.
  2. The elastic potential energy stored can be calculated using the equation:
  3. elastic potential energy = 0.5 × spring constant × (extension) 2
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What is the equation 1 2kx 2?

Other than Hooke’s Law, the equation for the potential energy function, U=1/2kx^2, is essentially used when determining the spring potential energy.

What is work done measured in?

One joule is defined as the amount of work done when a force of one newton is exerted through a distance of one meter. In the English system of units, where force is measured in pounds, work is measured in a unit called the foot-pound (usually abbreviated ft-lb).

How do you calculate work done by Young’s modulus?

Find the work done in stretching a wire of length 2 m and of sectional area 1 mm² through 1 mm if Young’s modulus of the material of the wire is 2 × 1011 N/m². Given: Area = A = 1 mm² = 1 × 106 m², Length of wire = L = 2m, Extension in wire = l = 1mm = 1 × 103 m, Young’s modulus = Y =2 × 1011 N/m².

What is half KX Square?

Brainly User. Answer: The work done on the system equals the area under the graph or the area of the triangle, which is half its base multiplied by its height, or W=12kx2 W = 1 2 kx 2.

When a spring is stretched by 2 cm It stores 100 J of energy if it is stretched further by 2 cm The stored energy will be increased by?

When the spring is stretched by 2 cm (=0.02 m), the stored energy is 100 J. We can find the value of spring constant k by putting the given values on the above equation. Now, if we stretch the spring further by 2 cm, x will be 4 cm (0.04 m).

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