Newton’s Laws and the Motion of Particles Teacher Excellence Workshop June 19, 2009

Introducing Forces A force is a push or pull on an object. When forces are unbalanced, they cause an object to accelerate, or to change its velocity by speeding up, slowing down, or changing direction.

Draw the forces for a physics book resting on a table FTFT FGFG Free Body Diagram Physics Book FTFT FGFG Force Diagram

Newton’s 1 st Law (Law of Inertia) If there is zero net force on a body, it cannot accelerate, and therefore must move at constant velocity. This means the body cannot turn. the body cannot speed up. The body cannot slow down.

Newton’s Second Law A body accelerates when acted upon by a net external force.The acceleration is proportional to the net force and is in the direction which the net force acts. ∑F = ma where ∑F is the net force measured in Newtons (N) m is mass (kg) a is acceleration (m/s 2 )

Working 1 st or 2 nd Law Problems 1. Identify the system acted upon by forces such that all parts of the system have the same acceleration. 2. Define a coordinate system. 3. Identify forces by drawing a force or free body diagram. 4. Explicitly write  F=ma (or  F=0) 5. Replace  F with the actual forces in your free body diagram. 6. Substitute numeric values, where appropriate, and solve for unknowns.

Sample problem: In a grocery store, you push a 14.5-kg cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 2.00 seconds?

Sample problem: In a grocery store, you push a 14.5-kg cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 3.00 seconds?

Newton’s Third Law For every action there exists an equal and opposite reaction. If A exerts a force F on B, then B exerts a force of -F on A. Newton’s Third Law must involve the forces exerted by bodies on each other.

Examples of Newton’s 3rd Law Copyright James Walker, “Physics”, 1 st edition

Sample Problem: You rest an empty glass on a table. a) Identify the forces acting on the glass with a free body diagram. b) Are these forces equal and opposite? c) Are these forces an action-reaction pair? Why or why not?

Sample Problem: You rest an empty glass on a table. a) Identify the forces acting on the glass with a free body diagram. b) Are these forces equal and opposite? c) Are these forces an action-reaction pair? Why or why not?

Requirements for Newton’s Laws The 1 st and 2 nd laws require that ONE system be analyzed and that ALL the forces on the system be accounted for. The 3 rd law requires that TWO systems be analyzed and that the forces of interaction between the two be accounted for.

Sample Problem: A force of magnitude 7.50 N pushes three boxes as shown. Find the acceleration of the system. Copyright James Walker, “Physics”, 1 st edition

Sample Problem: A force of magnitude 7.50 N pushes three boxes as shown. Find the acceleration of the system. Copyright James Walker, “Physics”, 1 st edition

Sample Problem: A force of magnitude 7.50 N pushes three boxes as shown. Find the force that box 2 exerts on box 3. Copyright James Walker, “Physics”, 1 st edition

Sample Problem: A force of magnitude 7.50 N pushes three boxes as shown. Find the force that box 2 exerts on box 3. Copyright James Walker, “Physics”, 1 st edition

Newton’s 2 nd Law in 2-D The situation is more complicated when forces act in more than one dimension. You must still identify all forces and draw your force diagram. You then resolve your problem into an x-problem and a y-problem (remember projectile motion????).

Problem: A skier skis down a slope with an acceleration of 3.50 m/s 2. If friction can be ignored, what is the angle of the slope with respect to the horizontal?

Sample problem: An object acted on by three forces moves with constant velocity. One force acting on the object is in the +x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the -y direction. Find the direction and magnitude of the third force acting on the object.

Sample problem: An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the negative y direction. Find the direction and magnitude of the third force acting on the object.