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Section 2 | Newtonian Mechanics Dynamics Learning outcomes describe the effect of balanced and unbalanced forces on a body Solve problems for a static-point mass Identify forces acting on an object and draw free-body diagrams

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Section 2 | Newtonian Mechanics Dynamics What are the effects of forces on motion? Balanced and Unbalanced Forces When forces acting on an object is balanced, there is no resultant force. No resultant force due to balanced forces

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Section 2 | Newtonian Mechanics Dynamics What are the effects of forces on motion? Balanced and Unbalanced forces When forces acting on an object is unbalanced, there will be a resultant force Resultant force due to unbalanced forces

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Resultant Force (of two perpendicular force)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added?

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Section 2 | Newtonian Mechanics Dynamics 3.3 How are forces acting in 2 dimensions added? Resultant Force (of two perpendicular force)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Resultant force (of 3 forces acting on an object in 2 dimensions) Unbalanced forces When 3 forces are applied to a point of an object, the resultant force (due to it being unbalanced) acting on the object can be obtained by adding the force vectors Vectors A,B and C represent three forces

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Unbalanced forces Resultant force (of 3 forces acting on an object in 2 dimensions)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Resultant force (of 3 forces acting on an object in 2 dimensions)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Balanced forces When 3 forces acting on an object is balanced, resultant force is 0 There is no acceleration An object will either stay at rest or move with constant velocity Resultant force (of 3 forces acting on an object in 2 dimensions)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Resultant force (of 3 forces acting on an object in 2 dimensions)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Resultant force (of 3 forces acting on an object in 2 dimensions)

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Section 2 | Newtonian Mechanics Dynamics How are forces acting in 2 dimensions added? Resultant force (of 3 forces acting on an object in 2 dimensions) Example Tom, Dick and Harry are pulling a metal ring. Tom pulls with a force of 100 N and Dick pulls with a force of 140 N at an angle of 70° to Tom. If the ring does not move, by scale drawing or other wise, determine what force Harry is exerting.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram A diagram which shows all the forces acting on a body is called a free-body diagram Consists primarily of a sketch of a body and arrows representing the forces acting on it Some of these examples are weight, contact force and tension We can use these to analyse the motion of the body

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : Weight Some common forces used in free- body diagrams Free-body diagrams Weight of a body The weight of a body is the gravitational force exerted by the Earth on the body. The weight acts at the center of gravity of a body. It is always directed towards the center of the Earth The free-body diagram of a body falling without air resistance is shown below.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : Contact force Some common forces used in free- body diagrams Free-body diagrams Contact force The contact force is the force exerted by the contact surface on the body. It acts perpendicularly to the contact surface. Two forces act on the body: they are the contact force and the weight. The free-body diagram is shown below.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : Tension Some common forces used in free- body diagrams Free-body diagrams Tension The tension is directed along the length of the string and pulls equally on the support and the pendulum bob. The diagram below is not a free-body diagram as it shows forces acting on three bodies: the pendulum bob, the string and the support. It will not be useful in analysis. To isolate the pendulum bob as a free- body, the only contact force acting on the bob is the tension. Hence, the free-body diagram of the pendulum bob consists of the tension and weight only. This is illustrated by the diagram below.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : The free-body diagram of the crate would consist of The weight of the crate, The tension force exerted on the crate, The contact force of the floor of the crate.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : Weight and contact force are equal. No resultant force acting vertically Acceleration of the crate is due entirely to the tension force

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : Now consider the situation of a man who has jumped up and is not in contact with the earth Situation for a man near the Earth

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Section 2 | Newtonian Mechanics Dynamics How do we analyse the effects ? Free-body diagram Example : The pair of action and reaction forces is the gravitational force by the Earth on the man and the gravitational force by the man on the Earth There are 2 free-body diagrams : One for the man and the other for the Earth Situation for a man near the Earth

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : The free-body diagram of the man shows the force acting on him only Free-body diagram for a man near the Earth

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : The free-body diagram for the Earth shows the force that acts on the Earth only Free-body diagram for the Earth near a man

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : Now consider the situation of a man standing on the Earth Situation for a man standing on the Earth

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : The first pair of action and reaction forces is the gravitational force by the Earth on the man and the gravitational force by the man on the Earth The second pair of action and reaction forces is the contact force by the man on the Earth and the contact force by the Earth on the man There are two free-body diagrams : One for the man and one for the Earth Situation for a man standing on the Earth

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : The free-body diagram shows two forces : F 1 and F 2 acting on the man. Since the man is at rest, the two forces are equal and opposite in direction Free-body diagram for a man standing on the Earth. The man is in equilibrium because the forces on him are equal and opposite.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Example : The free-body diagram for the Earth shows two forces, F 1 and F 2 acting on the Earth Since F 1 = F 2, the Earth is also at rest Free-body diagram for the Earth near a man. The Earth is in equilibrium because the forces on it are equal and opposite.

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Free-body diagram of the gymnast

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Free-body diagram of the beam

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Section 2 | Newtonian Mechanics Dynamics Free-body diagram Free-body diagram of the Earth

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