NEWTON’S THREE LAWS OF MOTION HANDOUT

Introduction – Sir Isaac Newton formulated three laws of motion that form the basis of classical mechanics and have direct applications in engineering and physics. The laws of motion describe the relation between the forces acting on a body and its motion due to those forces. The equations are fundamental tools used to understand and predict any motion of bodies or motion of objects in the engineering and scientific fields.

Law 1: Law of Inertia Formula: Fnet = ma Where Fnet is the net force, m is the mass of the object and a is the acceleration of the object due to the net force.

Worked example: A race car accelerates from 0 to 60 mph in 4 seconds. What is the net acceleration?

Given: vi = 0 mph vf = 60 mph t = 4 seconds

Solution: Using the equation v = at, we can solve for a: a = (vf-vi)/t a = (60-0)/4 a = 15 m/s2

Questions (5 on each law): Law 1: 1. What is inertia? 2. What is Newton’s first law of motion? 3. What is meant by the net force? 4. How do you calculate an objects acceleration due to a net force? 5. How does law of inertia relate to an objects motion?

Law 2: Law of Acceleration Formula: F= ma Where F is the force, m is the mass of the object and a is the acceleration of the object.

Worked example: An engineer is attempting to move a block of mass 20 kg across a flat surface by exerting a constant force of 50 newtons. What is the acceleration of the block?

Given: m = 20 kg F = 50 N

Solution: Using the equation F = ma, we can solve for a: a = F/m a = 50/20 a = 2.5 m/s2

Questions (5 on each law): Law 2: 1. What is Newton’s second law of motion? 2. What is the formula used to describe this law? 3. How is force related to the acceleration of an object? 4. How do you calculate the acceleration of an object given its force and mass? 5. How does the law of acceleration relate to engineering?

Law 3: Law of Action and Reaction Formula: FAB = -FBA Where FAB is the force of object A on object B and FBA is the force of object B on object A.

Worked example: A car of mass 3,500 kg is driving at a constant speed when it bumps into a wall. The wall applies a force of 2,500 N on the car. What force is the car applying to the wall?

Given: m = 3,500 kg Fwall on car = 2,500 N

Solution: Using the equation FAB = -FBA, we can solve for Fcar on wall: Fcar on wall = -Fwall on car Fcar on wall = - 2,500 N Fcar on wall = -2,500 N

Questions (5 on each law): Law 3: 1. What is Newton’s third law of motion? 2. What is the formula used to describe this law? 3. How is the force of object A on object B related to the force of object B on object A? 4. How do you calculate the force of object B on object A given the force of object A on object B? 5. How does the law of action and reaction relate to engineering?

Numerical Questions (10 questions): 1. An engineer is attempting to move a block of mass 25 kg across a flat surface by exerting a constant force of 80 newtons. What is the acceleration of the block? 2. A bridge is suspended from 3 cables. Each cable supports a force of 2,000 N. What is the total force on the bridge? 3. A jet of mass 3,000 kg is flying at a constant velocity when it is bumped by an air pocket. The air pocket applies a force of 800 N on the jet. What force is the jet applying to the air pocket? 4. A car of mass 1,400 kg accelerates from 0 to 30 m/s in 5 seconds. What is the net acceleration? 5. An engineer is attempting to move a block of mass 12 kg across a flat surface by exerting a force of 40 newtons. What is the acceleration of the block? 6. A jet of mass 4,000 kg is flying at a constant velocity when it is bumped by an air pocket. The air pocket applies a force of 1,200 N on the jet. What force is the jet applying to the air pocket? 7. A rocket of mass 8,000 kg accelerates from 0 to 10 m/s2 in 10 seconds. What is the net force? 8. A race car accelerates from 0 to 75 mph in 7 seconds. What is the net acceleration? 9. A bridge is suspended from 4 cables. Each cable supports a force of 1,500 N. What is the total force on the bridge? 10. A car of mass 2,500 kg accelerates from 0 to 20 m/s in 4 seconds. What is the net acceleration?