Newtonian Mechanics and Impulse

Friction on an Inclined Plane

When an object slides down an inclined plane at a constant speed, the forces acting on it are balanced. The frictional force opposes the component of gravity parallel to the incline.

• Key Terms: Frictional force is the force that resists the motion of an object in contact with a surface.

• Constant speed implies zero acceleration, so the net force along the incline is zero.

• The gravitational force parallel to the incline is given by:

• The frictional force must balance this component:

• Example: For a 1.5 kg block on a 30° incline,

Spring-Loaded Launch and Conservation of Energy

When an object is launched by a compressed spring, the potential energy stored in the spring is converted into kinetic energy and gravitational potential energy as the object moves.

• Spring Potential Energy:

• Conservation of Energy: The total mechanical energy is conserved if there is no friction:

• Example: If a puck is launched by a spring compressed by and rises to a height , set the initial spring energy equal to the sum of kinetic and potential energy at height $h$ to solve for the speed .

Impulse and Change in Velocity

Impulse is the product of force and the time over which it acts. It is equal to the change in momentum of an object.

• Impulse:

• For the same impulse applied to different masses, the change in velocity is:

• Key Point: The object with the smallest mass will experience the largest change in velocity for the same impulse.

• Example: If four balls of different masses receive the same impulse, the lightest ball will have the greatest change in velocity.

Comparing Impulse Effects

Additional info: The table above illustrates that for a fixed impulse, the change in velocity is inversely proportional to the mass of the object.

Summary of Key Equations

• Friction on an incline:

• Spring energy:

• Conservation of energy:

• Impulse: