Review Hooke's law describes an ideal spring, Many real springs are better described by the restoring force (Fsp),--kAs- q(As), where q is a constant. Consider a spring with k = 350 N/m and 9=750 N/m Part A How much work must you do to compress this spring 15 cm? Note that, by Newton's third law, the work you do on the spring is the negative of the work done by the spriıng Express your answer with the appropriate units. • View Available Hint(s) W = 4.0 J Submit Previous Answers v Correct Part B By what percent has the cubic term increased the work over what would be needed to compress an ideal spring? Express your answer as a percentage. > View Available Hint(s) AW = 2.35 Submit
Kinematics
A machine is a device that accepts energy in some available form and utilizes it to do a type of work. Energy, work, or power has to be transferred from one mechanical part to another to run a machine. While the transfer of energy between two machine parts, those two parts experience a relative motion with each other. Studying such relative motions is termed kinematics.
Kinetic Energy and Work-Energy Theorem
In physics, work is the product of the net force in direction of the displacement and the magnitude of this displacement or it can also be defined as the energy transfer of an object when it is moved for a distance due to the forces acting on it in the direction of displacement and perpendicular to the displacement which is called the normal force. Energy is the capacity of any object doing work. The SI unit of work is joule and energy is Joule. This principle follows the second law of Newton's law of motion where the net force causes the acceleration of an object. The force of gravity which is downward force and the normal force acting on an object which is perpendicular to the object are equal in magnitude but opposite to the direction, so while determining the net force, these two components cancel out. The net force is the horizontal component of the force and in our explanation, we consider everything as frictionless surface since friction should also be calculated while called the work-energy component of the object. The two most basics of energy classification are potential energy and kinetic energy. There are various kinds of kinetic energy like chemical, mechanical, thermal, nuclear, electrical, radiant energy, and so on. The work is done when there is a change in energy and it mainly depends on the application of force and movement of the object. Let us say how much work is needed to lift a 5kg ball 5m high. Work is mathematically represented as Force ×Displacement. So it will be 5kg times the gravitational constant on earth and the distance moved by the object. Wnet=Fnet times Displacement.
![**Hooke's Law and Spring Compression**
**Overview:**
Hooke's law describes the behavior of an ideal spring, relating the force needed to compress or extend a spring to the distance it is stretched. However, some real springs exhibit additional restoring forces, described by the equation:
\[ F_{SP} = -kΔs - q(Δs)^3 \]
where \( k \) is the spring constant and \( q \) is a parameter accounting for nonlinearity.
Given values:
- \( k = 350 \, \text{N/m} \)
- \( q = 750 \, \text{N/m}^3 \)
**Part A: Calculating Work for Spring Compression**
*Question:*
How much work must you do to compress this spring by 15 cm (0.15 m)? According to Newton's third law, the work you do on the spring is the negative of the work done by the spring.
*Solution:*
Express your answer with the appropriate units:
The calculated work \( W \) to compress the spring is given as 4.0 J (joules).
**Part B: Effect of Nonlinearity on Spring Work**
*Question:*
By what percentage has the cubic term increased the work over what would be needed to compress an ideal spring?
*Solution:*
Express your answer as a percentage:
The percent increase in work due to the cubic term is calculated as 2.35%.
This illustrates how the cubic term affects the energy needed compared to an ideal spring model.
**Conclusion:**
Understanding these concepts allows students to appreciate deviations from ideal behaviors in real-world applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7859f905-a93a-424f-a5cf-092dfae20bfb%2F6770a8cc-798f-490d-952c-32415bb5fc12%2F8mzfnca_processed.jpeg&w=3840&q=75)
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