Evans SPH 4U1

Unit 4: Energy & Momentum

Note 2: Elastic Potential Energy

Reference: Chapter 4.5 (note we will NOT cover simple harmonic motion - we cover it later with waves)

When forces are applied to an object, the dimensions of the object tend to change.  For example, if opposite forces are applied to both ends of a spring, it stretches or compresses.  When the forces are removed the spring returns to its original length. If an object returns to its original dimensions after the applied force is removed, we say that the object is elastic. The British scientist, Robert Hooke, was one of the first to study the elasticity of matter.

Hooke's Law:

The magnitude of the force on the spring is proportional to the distance the spring has moved from equilibrium.

where F is the force exerted on the spring, x is the amount of deformation of the spring, k is proportionality constant.

when the spring is compressed, both F and x are negative

Elastic Potential Energy:

The energy stored in an object that is stretched or compressed (also equal to work done in compressing or stretching the spring).

It can be transformed into other forms of energy like kinetic energy.

Fx

x         Area under a Force-Displacement graph is work

Since this work has been transformed into elastic potential energy,

Example 1:

What force is necessary to stretch a spring, horizontally, whose force constant is 120 N/m by an amount of 30 cm? 36N

Example 2:

A spring whose force constant is 48 N/m has a 0.25 kg mass suspended from it. What is the extension of the spring? 5.1 cm

Example 3:

The force applied to a dynamics cart is measured with a stretched spring. What is the acceleration of a 2.0 kg cart on a flat, frictionless surface if pulled by a spring with a force constant of 40N/m, stretched by a constant amount of 8.0 cm? 1.6 m/s2

Example 4:

You stretch a spring horizontally a distance of 15 mm by applying a force of 0.18N[E].

a) Find the force constant of the spring. 12 N/m

b) What is the force exerted by the spring on the student? 0.18N[W]

Example 5:

You shoot a block from a compressed spring up a ramp.  The block has a mass of 2.0 x 10-2 kg. The spring's force constant is 8.0 N/m.  Friction is negligible.

a) If the block slides up the ramp through a vertical height of 4.0 x 10-2 m, how much must the spring be compressed? 4.4 x 10-2m

b) If friction was involved would the answer be more, less or the same? more

**Example 6:

A horizontal spring with a force constant of 10 N/m is mounted on a table ledge to shoot marbles at targets of the floor 1.0m below.  A marble of mass 10 x 10-3 kg is shot from the spring, which is compressed a distance of 4.0 cm.  How far does the marble travel before hitting the floor? 0.57m

Homework:

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