FORCES AND MOTION

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After studying this topic, you are expected to be able to:

Apply Newton's Laws as basic principles for dynamics of particle in linear motion and vertical motion.

State each of Newton's laws of motion

Describe the definitions and types of forces acting on a body in different situation (pulley, inclined surface, tension of string)

Apply F = m.a in solving problems related to linear motion of a body

Apply F = m.a in solving problems related to vertical motion of a body

Analyze relation between force and its frictional force

Analyze the coefficient of frictional force (static and kinetic friction) through inclined plane

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What is Force?

Force PUSH/ PULL

unit: newton (kg.m/s2)

It is a VECTOR QUANTITY

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Types of Force:

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How to deal with forces?

Free Body DiagramTo keep things simple only draw forces that

acting on the object

Example:N

Frictional force (f)

W

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Exercise:

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Force is Vector, so….

Calculate forces : calculate vectors!

Example:

How to calculate forces?

A body is pulled in two opposing directions by two ropes as shown in Figure beside. The resultant force acting is the vector sum of the forces.

If a body is pulled by two perpendicular ropes as in Figure 2.33, then the vector addition is solved using vectors addition.

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Exercise:

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Forces Balanced Equilibrium

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Forces Balanced Equilibrium

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Forces Balanced Equilibrium

Another example:

Separate the vectors into 2 components: x & y

If the box is in equilibrium, then:Total component in x = 0 forces left = forces rightTotal component in y = 0 forces up = forces down

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Example:

Consider the situation below. If the forces on this box are balanced:a) write an equation for the components of the forces

parallel to the rampb) write equation for the forces perpendicular to the rampc) find the friction (F) & normal force (N)

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Example:

A ball of weight 10 N is suspended on a string and pulled to one side by another horizontal string as shown beside. If the forces are balanced:(a) write an equation for the horizontal components of the forces acting on the ball(b) write an equation for the vertical components of the forces acting on the ball(c) use the second equation to calculate the tension in the upper string, T(d) use your answer to (c) plus the first equation to find the horizontal force F.

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Example:

A rock climber is hanging from a rope attached to the cliff by two bolts as shown in Figure beside. If the forces are balanced

a) write an equation for the vertical component of the forces on the knot

b) write an equation for the horizontal forces exerted on the knot

c) calculate the tension T in the ropes joined to the bolts. The result of this calculation shows why ropes should not be connected in this way.

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Newton’s Laws of MotionForces balanced object is at rest (?)

Forces not balanced object moves (?)

How do we explain that with strong argument?

Newton’s Laws of Motion

1st Law:

A body will remain at rest or moving with constant velocity unless acted upon by an unbalanced force.

Net force = 0 no acceleration

Σ � = �18

Example:

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Example:

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Constant velocity Net force = 0

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Example:

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Example:

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Application of 1st Law:

Seat Belts mechanism

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Note:

If the forces are balanced, will the object always be at rest or moving with constant velocity?

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2nd Law:

The acceleration of an object is

directly proportional to the net force acting on it and inversely proportional to its mass.

Σ � = �.�

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Example:

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Example:

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Example:

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• Simple Pulley system

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Example:

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Single isolated force can’t exist

Pair of forces on

two different objects

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3rd Law:

If body A exerts a force on body B then body B will exert an equal and opposite force on body A.

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Example:A car of mass m is on an icy driveway inclined at an angle q=30.0o, as in Figure 4.16a. Determine (a) theacceleration of the car, assuming that the incline is frictionless. (b) If the length of the driveway is 20.0 m and the car starts from rest at the top, how long does it take to travel to the bottom? (c) What is the car’s speed at the bottom?

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Frictional Force

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A frictional force vector sum of many forces acting

between the surface atoms of one body and those of

another body

Types of Frictional Force:Static Friction (fs)

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Kinetic Friction (fk)

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Note:fs max > fk

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Static Frictional Force:

fs ≤ ms.N

Maximum static frictional force: in verge of slipping

fs max = ms.N

ms= coefficient of static friction depend on the nature of surfaces

N = Normal force

Kinetic Frictional Force:

fk = mk.N

mk= coefficient of kinetic friction47

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Example:1. The hockey puck in Figure 4.22, struck by a hockey stick, is given an initial speed of 20.0 m/s on a frozen pond. The puck remains on the ice and slides 120 m, slowing down steadily until it comes to rest. Determine the coefficient of kinetic friction between the puck and the ice.

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Suppose a block with a mass of 2.00 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is 0.30, what maximum angle can the ramp make with the horizontal before the block starts to slip down?

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a. Maximum static friction between sled and plane.

b. Magnitude of the force required in order to make the sled stay at rest, not sliding down the plane. (remember, there are frictional force and weight of object)

c. What is the minimum magnitude F that will start the sled moving up the plane? (Hint: draw the force first)

d. What value of F is required to move the sled up the plane at constant velocity?

A loaded penguin sled weighing 40√2 N rests on a plane inclined at angle q = 45° to the horizontal (Figure beside). Between the sled and the plane, the coefficient of static friction is 0.25, and the coefficient of kinetic friction is 0.15. Determine:

A block with mass m1 = 4.00 kg anda ball with mass m2 = 7.00 kg are connected by a light string that passes over a frictionless pulley, as shown in Figure 4.23a. The coefficient of kinetic friction between the block and the surface is 0.300.Find the acceleration of the two objects and the tension in the string.

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