the potential energy of a spring..when stretched by 4 cm is u..when stretched by 20 cm it will ?

It is stretched 5 times farther and since they are asking about potential energy I am going to assume that means u will be multiplied by 5.


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To determine the potential energy of a spring when stretched by a different amount, we can use Hooke's Law and the formula for potential energy stored in a spring.

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, it can be expressed as:

F = kx

where F is the force applied by the spring, k is the spring constant, and x is the displacement of the spring.

The potential energy stored in a spring is given by the formula:

U = (1/2)kx^2

where U is the potential energy, k is the spring constant, and x is the displacement of the spring.

Now, let's calculate the potential energy when the spring is stretched by 4 cm and denoted as U1.

Given that the displacement of the spring is 4 cm (0.04 m), we can use Hooke's Law to find the force exerted by the spring.

F1 = k * 0.04

Next, we can plug this force into the potential energy formula:

U1 = (1/2) * k * (0.04)^2

Now, let's calculate the potential energy when the spring is stretched by 20 cm and denoted as U2.

Given that the displacement of the spring is 20 cm (0.2 m), we can use Hooke's Law again to find the force exerted by the spring.

F2 = k * 0.2

Similarly, we can plug this force into the potential energy formula:

U2 = (1/2) * k * (0.2)^2

Therefore, by substituting the values into the equations, we can find the potential energy of the spring when stretched by 20 cm.