Suppose that 5 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 51 cm. (a) How much work is needed to stretch the spring from 41 cm to 46 cm? (Round your answer to two decimal places.) 5 Incorrect: Your answer is incorrect. J (b) How far beyond its natural length will a force of 25 N keep the spring stretched? (Round your answer one decimal place.) cm

a) 0.6 joules of work are needed to stretch the spring from 41 centimeters to 46 centimeters.

b) The spring must be 5.6 centimeters far from its natural length.

Step-by-step explanation:

a) The work done to stretch the ideal spring from its natural length is defined by the following definition:

(1)

Where:

- Spring constant, measured in newtons.

, - Initial and final lengths of the spring, measured in meters.

- Work, measured in joules.

The spring constant is: (, , )

If we know that , and , then the work needed is:

0.6 joules of work are needed to stretch the spring from 41 centimeters to 46 centimeters.

b) The elastic force of the ideal spring (), measured in newtons, is defined by the following formula:

(2)

Where is the linear difference from natural length, measured in meters.

If we know that and , then the linear difference is:

The spring must be 5.6 centimeters far from its natural length.

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol