PHYSICS 197 Section 1 Chapter N1 Newton’s Laws October 6, 2017

Review of C14 Elastic and Inelastic Collisions I−D inelastic: I−D elastic:

Two-Dimensional Collision Conservation of Momentum: Conservation of Energy: Demo: Newton’s craddle and Ballistic Pendulum Completely inelastic: θ0 and fraction  ½. Elastic Limit: θ450 and fraction 0.

Slingshot Effect

Slingshot Effect

Outline of N1 Newtonian Synthesis Newton’s Laws of Motion Vector Calculus Formal Definitions of Velocity and Acceleration Uniform Circular Motion

Newtonian Synthesis How do interactions affect the motion of an object? Prior to Newton, different laws of motion were thought to apply to terrestrial and celestial objects. Using the findings of Galileo and Kepler, Newton demonstrated that the laws of physics are universal. His Principia book transformed physics from a branch of natural philosophy into a quantitative science. One of mankind’s greatest intellectual achievements.

Newton’s Laws of Motion In the absence of external interactions, an object’s (or system’s) center of mass moves at a constant velocity. The net external force on a system causes that system’s center of mass to accelerate at a rate inversely proportional to its total mass. The force that a given interaction between objects 1 and 2 exerts on 1 is equal in magnitude and opposite in direction to the force it exerts on 2. These laws express implications of the principle of momentum transfer (or conservation of momentum).

1st Law In the absence of external interactions, an object’s (or system’s) center of mass moves at a constant velocity. A system’s momentum can be calculated from its center-of-mass velocity: Plays an essential role in the definition of inertial reference frame.

2nd Law The net external force on a system causes that system’s center of mass to accelerate at a rate inversely proportional to its total mass.

3rd Law The force that a given interaction between objects 1 and 2 exerts on 1 is equal in magnitude and opposite in direction to the force it exerts on 2.

Clicker Question Suppose a 10,000-kg truck traveling at 65 mph hits a parked 500-kg Volkswagen Beetle. Which vehicle exerts the stronger force on the other during the collision? The truck The Beetle Both forces have equal magnitude. There is no way to tell.

Answer Suppose a 10,000-kg truck traveling at 65 mph hits a parked 500-kg Volkswagen Beetle. Which vehicle exerts the stronger force on the other during the collision? The truck The Beetle Both forces have equal magnitude. There is no way to tell. Explanation: Newton’s 3rd law requires this, even though counterintuitive! Just because forces are same doesn’t mean the objects’ response (change in velocity) must be same.

Clicker Question N1T.5 A parent pushes a small child on a swing so that the child moves rapidly away while the parent remains at rest. How does the magnitude of the force that the child exerts on the parent compare to the magnitude of the force that the parent exerts on the child? The force on the child is larger in magnitude. The force on the parent is larger in magnitude. These forces have equal magnitude. The child exerts zero force on the parent. There is no way to tell.

Answer N1T.5 A parent pushes a small child on a swing so that the child moves rapidly away while the parent remains at rest. How does the magnitude of the force that the child exerts on the parent compare to the magnitude of the force that the parent exerts on the child? The force on the child is larger in magnitude. The force on the parent is larger in magnitude. These forces have equal magnitude. The child exerts zero force on the parent. There is no way to tell. Explanation: Newton’s 3rd law requires this, even though other forces on the parent (mostly friction) keep her from moving in response to the force exerted by the child.

Vector Calculus We don’t have to invent it from scratch the way Newton did!

Instantaneous Velocity Rate of change of displacement

Average Velocity The shorter the time interval, the closer the direction of the average velocity to the instantaneous velocity.

Instantaneous vs. Average

Acceleration Rate of change of velocity Average acceleration:

Clicker Question N1T.13 An object falling vertically at a speed of 20 m/s lands in a snowbank and comes to rest 0.5 s later. The object’s average acceleration during this interval is Upward Downward Zero Need more info.

Answer N1T.13 An object falling vertically at a speed of 20 m/s lands in a snowbank and comes to rest 0.5 s later. The object’s average acceleration during this interval is Upward Downward Zero Need more info. Explanation: Velocity goes from being downward to zero, so change in velocity is upward.

Circular Motion Centripetal acceleration An object moving in a circle must experience a net inward force.

Practice Problem N1R.3 Suppose you are driving on a large, dark parking lot in the middle of the night. Your headlights suddenly illuminate a wall directly ahead of you that is perpendicular to your direction of travel and stretching away on both sides as far as you can see. To avoid hitting the wall, is it better to turn your car to the right or left without braking or to brake as hard as you can while moving in a straight line toward the wall?

Solution