Applying Newton’s Laws

A systematic approach for 1st or 2nd Law Problems1. Identify the system to be analyzed. This

may be only a part of a more complicated system. This is really the most important step.

2. Select a reference frame or coordinate system, stationary or moving, but not accelerating, within which to analyze your system.

3. Identify all forces acting on the system. Ignore the others. This is best done by drawing!

4. Set up ΣF = ma equations for each dimension. Solve for relevant unknowns.

5. Use kinematics or calculus where necessary to calculate more about the motion.

• Sample Problem: A 5.00-g bullet leaves the muzzle of a rifle with a speed of 320 m/s. The bullet is accelerated by expanding gases while it travels down the 0.820 m long barrel. Assuming constant acceleration and negligible friction, what is the force on the bullet?

• Sample Problem: A 3.00 kg mass undergoes an acceleration given by a = (2.50i + 4.10j) m/s2. Find the resultant force F and its magnitude.

Normal force

•The force that keeps one object from invading another object is called the normal force.

•“Normal” means “perpendicular”.•Always determine the normal force by

considering all forces that have components perpendicular to a surface.

Problem: determine the normal force acting on a 5.0 kg box sitting on a flat table.

Problem: Now determine the normal force acting on a 5.0 kg box sitting on a flat table.

F=16 N

40°

Problem: Now determine the normal force acting on a this 5.0 kg box sitting on a ramp at angle q=30o.

Problem: Assume that the ramp is frictionless. What is the acceleration of the block down the ramp?

30o

F=20 N

20°

Tension

•A pulling force.•Generally exists in a rope, string, or cable.

•Arises at the molecular level, when a rope, string, or cable resists being pulled apart.

Tension (static 2D)

The sum of the horizontal and vertical components of the tension are equal to zero if the system is not accelerating.

15 kg

30o 45o

32 1

Problem: Determine the tension in all three ropes.

15 kg

30o 45o

32 1

Problem: What is the tension is the cable attached to a 5,000 kg elevator that starts on the ground floor at rest and accelerates upward, reaching a speed of 3.0 m/s in 2 seconds?

M

Pulley problems

•Pulley’s simply bend the coordinate system

m1

m2

Sample problem: derive a formula for acceleration, assuming the table is frictionless.

m1

m2

m 1 m2

q

Sample problem: derive a formula for acceleration, assuming the table is frictionless.

m 1 m2

q

Sample problem: derive a formula for the tension T in the string.

Atwood machine

•A device for measuring g.•If m1 and m2 are nearly the

same, slows down freefall such that acceleration can be measured.

•Then, g can be measured.m1

m2

Problem: For the Atwood machine shown, derive an equation which can be used to find g, the gravitational acceleration, from a measured value of acceleration.

m1

m2