A spring has a spring stiffness constant k of 80.0 N/m . How much must this spri

Question

A spring has a spring stiffness constant k of 80.0 N/m .

How much must this spring be compressed to store 50.0 J of potential energy?

x=?

Experiment 4: Newton's Second Law In the ey path in OBJECTIVES Newton's second law predicts that acceleration is a function of force and mass. To test thi mathematical relationship, a good experiment must isolate each contributing component an independently of the others. In this experiment, you measure the acceleration of an object b varying the force acting upon the object without changing its mass and by varying the objec' without changing the force. The objectives of this experiment are as follows: 1. To measure the linear acceleration of objects acted on by external forces 2. To predict the acceleration of an object by applying Newton's Second law. 3. To test the predictions using calculations and graphical methods THEORY Newton's second law in vector form is shown in equation 4.1. Newton's second law F. Here Fis the net force acting on an object, m is the mass of the object, and ã is its acceleration. If the force is constant, as, for instance, the force of gravity, the object moves with constant acceleration. Newton's second law also applies to systems of bodies considered as a whole, like two masses connected by a cord. Each of the objects in this experiment moves along a straight line. Thus it is sufficient to consider projections of the vectors on the direction of motion and we can remove the vector notation: F-ma In this experiment we measure the acceleration of a system consisting of a glider moving along a nearly frictionless air track, and a falling/hanging mass tied to the glider via a cord. The net force on the system is exerted by the gravitational force If you ignore friction, equation 4.2 acting on the hanging mass over a low-friction pulley the acceleration of the system according to Newton's second law is shown in Acceleration of the glider a g (4.2) Here nm is the hanging mass, M is the total moving mass, and g is the free-fall acceleration due to gravity The acceleration of an object is the rate of change in its velocity. If the velocity changes by an amount Av during a time A, the average acceleration is shown in equation 43. Average Acceleration (4.3) Here : 4-4and ,_r.ry-yW. Ifarbecomes very small, equation 4.3gives the instantancous acceleration at 44 For the motion with constant acceleration that we study in this experiment, the average and instantaneous accelerations are the same.

Explanation / Answer

elastic potential energy u = 0.5 kx^2

50 = 0.5 * 80* x2

X2 = 1.25

X = 1.118 m

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