**Evans SPH 4U1**

**Physics Grade 12**

**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.

F_{x
}

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/s ^{2}**

**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 ^{-2}m**

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:**

Page 211 #12, 13

Page 219 #8. 9. 11