CH 4.1 – 4.2 Resistance in Mechanical and Fluid System

4.1 ObjectivesState Newton’s second law of motion and use it

to solve problems involving force, mass, acceleration

Calculate an object’s weight given its mass

Explain the difference between static and kinetic friction

Explain how lubrication and rolling reduce friction

Newton’s 2nd Law of Motion

The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object

a = F / m F = ma m = f / a

1 N = (1 kg ) (1 m/s2) 1 lb = (1 slug) (1 ft/s2)

Newton’s 2nd Law and a Car’s MotionIn performance testing, a 1250-kg car

accelerates from 0 to 100 km/hr in 8.2 seconds. What is the average net force pushing the car during the test?

Example 1 SolutionConvert velocity to m/s :

(100 km) (1000 m ) (1 hr) = 27.78 m / s

1hr 1 km 3600 sec

Determine the car’s acceleration :

a= (Vf – Vi) / t

a= (27.78 m/s – 0 m/s) / 8.2 s

a= 3.39 m/s2

Calculate the force

F = ma (1250-kg) (3.39 m/s2) = 4237.5 N

Weight and MassThe weight of an object is = (mass)

(acceleration due to gravity)

Fg = mg

Acceleration due to gravity:

9.80 m/s2 32.2 ft/s2

Example 2A 65-kg person stands on a bathroom scale.

What force does the scale exert on the person?

(Think of Newton’s 3rd Law of Motion)

Example 2 SolutionFscale = Fg

Fg = m g

= (65 kg) (9.8 m/s2)

= 637 N

Example 3The same 65-kg person is placed on a scale in

an elevator. The elevator accelerates upward at a rate of 2.5 m/s2. What weight does the scale read while the elevator is moving?

Still consider Newton’s 3rd Law of Motion

Example 3 Solution Fscale = Fnet + Fg

= ma + mg

= m(a + g)

= 65 kg (2.5 m/s2 + 9.80 m/s2)

= 65 kg (12.3 m/s2)

= 799.5 N

What would the scale reading be if the elevator were accelerating downward at the same rate?

Calculating Distance using Gravity

Distance = ½ g t2

Accelg = (2d) / t2

Time = √ (2d) / a

Example 4Wiley coyote pushes a 0.32 kg stone from a cliff

123 ft high. If the acceleration due to gravity is 30.1 ft/s2, how long must the Road Runner “beep-beep” be standing still below?

Why is the acceleration due to gravity less than the described value of 32.2 ft/s2 ?

FRICTION

When a force is exerted on an object, inertia must be overcome for there to be a change in the motion of an object.

Friction must also be overcome for a stationary object to be moved.

What happens to much of the energy applied to a system when friction is present?

What can be done to reduce friction in a system?

Types of FrictionStatic Friction

The initial force of friction that must be overcome to start movement

Kinetic frictionThe second form of friction that must be overcome

to keep the object moving at a constant rate of speed

Think of the coefficient of friction as how slippery the surface of an object is.

Which joint has the most friction? What do is this condition known as?