When a small ball rolls horizontally off the edge of a surface, it embarks on a captivating journey that encompasses both horizontal and vertical motion. This phenomenon, known as projectile motion, unveils the intricate interplay between velocity, displacement, and time, while showcasing the fundamental principles of energy conservation.
As the ball leaves the edge, its horizontal velocity remains constant, while its vertical velocity undergoes a continuous change due to the influence of gravity. The ball’s trajectory, a graceful arc, is determined by the interplay of these two components of motion.
Introduction: A Small Ball Rolls Horizontally Off The Edge
A small ball is set in motion by rolling it horizontally off the edge of a table. The ball rolls off the table with an initial velocity of 1 m/s and lands on the floor 0.5 m below.
Horizontal Motion
The horizontal motion of the ball is described by the following equation:
“`v = u + at“`
where:
- v is the final velocity of the ball
- u is the initial velocity of the ball
- a is the acceleration due to gravity (9.8 m/s^2)
- t is the time taken for the ball to travel horizontally
Vertical Motion
The vertical motion of the ball is described by the following equation:
“`v = u + at“`
where:
- v is the final velocity of the ball
- u is the initial velocity of the ball
- a is the acceleration due to gravity (9.8 m/s^2)
- t is the time taken for the ball to travel vertically
Impact with the Ground
When the ball hits the ground, it experiences a force that is equal to the force of gravity acting on the ball. This force causes the ball to rebound from the ground.
The coefficient of restitution is a measure of the elasticity of a surface. It is defined as the ratio of the velocity of the ball after impact to the velocity of the ball before impact.
Post-Impact Motion
After the ball rebounds from the ground, it continues to move in a parabolic trajectory. The velocity of the ball after impact is less than the velocity of the ball before impact.
The factors that affect the post-impact velocity and trajectory of the ball include:
- The coefficient of restitution of the surface
- The initial velocity of the ball
- The angle at which the ball hits the surface
Energy Considerations
The total energy of the ball is conserved during its motion. The kinetic energy of the ball is converted to potential energy as the ball rises into the air. The potential energy of the ball is converted to kinetic energy as the ball falls back to the ground.
FAQ Overview
What factors influence the horizontal velocity of the ball?
The horizontal velocity of the ball is primarily determined by its initial velocity and the absence of significant air resistance.
How does gravity affect the ball’s vertical motion?
Gravity imparts a constant downward acceleration to the ball, causing its vertical velocity to increase as it falls.
What is the coefficient of restitution?
The coefficient of restitution is a dimensionless quantity that measures the elasticity of a surface and determines the amount of energy lost during impact.
