ELASTIC FORCE The force Fs applied to a spring to stretch it or to compress it an amount x is directly proportional to x. Fs = - k x Units: Newtons (N) Where k is a constant called the spring constant and is a measure of the stiffness of the particular spring. The spring itself exerts a force in the opposite direction:

This force is sometimes called restoring force because the spring exerts its force in the direction opposite to the displacement. This equation is known as the spring equation or Hooke’s Law.

The elastic potential energy is given by: PEs = ½ kx2 Units: Joules (J)

Energy Transformations Work done by a spring v m m k x

Energy Transformations Work done by friction v = 0 m m k x d

A dart of mass 0.100 kg is pressed against the spring of a toy dart gun. The spring (k = 250 N/m) is compressed 6.0 cm and released. If the dart detaches from the spring when the spring reaches its normal length, what speed does the dart acquire? m = 0.1 kg k = 250 N/m x = 0.06 m Us = K ½ kx2 = ½ mv2 = 3 m/s