  Problem solving tips

## Laws Of Motion

- Become an expert problem solver
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Free Body Diagrams
A free body diagram is a visual representation of all the forces acting on an object. It is a simple way analyze the dynamics of an object by deconstructing all the forces acting on an object and studying the object as if it were in isolation. Let us understand how to draw a free body diagram for any system:
1. Observe the object under consideration. Draw the object with its basic geometry, without any details, such that it is isolated from all elements around it.
Note: While making a free body diagram of connected objects, we can draw separate diagrams for each object  2. Now list all the external forces directly acting on the body. A free body diagram does not include internal forces of an object. External forces like, weight, reaction force, friction etc. are to be included in the free body diagram.
3. Represent all these forces acting on the objects as vectors with their correct orientation along with the object.
Note: Any acceleration possessed by the body is not to be included in the free body diagram as the acceleration arises from all the forces seen in the free body diagram being unbalanced.  Sample Problems:
A point  on a sphere of weight  rests in contact with a smooth vertical wall and is supported by a string joining a point  on the sphere to a point  on the wall. Draw a free body diagram of the sphere.
A rod OA is suspended with help of a massless string AB as shown in figure. Rod is hinged at point O. Draw free body diagram of the rod.
A helicopter is moving to the right at a constant horizontal velocity. It experience three forces , and force on it caused by rotor . Which of the following diagrams can be a correct free-body diagram representing force on the helicopter?
A
B
C
D
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Tip 2: How to write the Second Law equation using a free-body diagram?
Now that you know how to draw the free body diagram, how can you apply Newton's Second Law to it.
Let's checkout the previous example.  Let us find out how to write the Second Law equation for both blocks separately.  3
Tip 3: Solving problems in mechanics
Let us learn how to deconstruct a simple problem in mechanics to understand the dynamics of a mechanical system. Let us assume, we want to determine the acceleration of a block sliding down on a frictionless plane. How shall we approach this problem?  Sample Problems:
A block is placed on top of a block (Fig. above). A horizontal force of is applied to the block, and the block is tied to the wall. The coefficient of kinetic friction between all moving surfaces is . (a) Draw a free-body diagram for each block and identify the actionreaction forces between the blocks. (b) Determine the tension in the string and the magnitude of the acceleration of the block.
Two blocks connected by a rope of negligible mass are being dragged by a horizontal force (Fig. above). Suppose , and the coefficient of kinetic friction between each block and the surface is . (a) Draw a free-body diagram for each block. Determine (b) the acceleration of the system and (c) the tension in the rope.
Three objects are connected on a table as shown in above figure. The coefficient of kinetic friction between the block of mass and the table is . The objects have masses of , and and the pulleys are frictionless. (a) Draw a free body diagram of each object. (b) Determine the acceleration of each object, including its direction. (c) Determine the tensions in the two cords. What If? (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain.
A woman at an airport is towing her suitcase at constant speed by pulling on a strap at an angle above the horizontal (Fig. above). She pulls on the strap with a force, and the friction force on the suitcase is . (a) Draw a free body diagram of the suitcase. (b) What angle does the strap make with the horizontal? (c) What is the magnitude of the normal force that the ground exerts on the suitcase?
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Tip 4: Elevator Problem
The force we exert on the a weighing machine determines our weight on the scale. On a stationary weighing machine the reaction force offered is the same as the actual weight mg. However if the weighing machine is accelerating upwards or downwards, it causes the reaction force to change , which shows an apparent change in weight on the scale. Lets simplify how to approach questions related to the apparent weight inside an elevator by drawing the free body diagram in different cases.    Sample Problems:
Mandy stands on a weighing scale inside a lift (elevator) that accelerates vertically upwards as shown in the diagram below. The forces on Mandy are her weight W and the reaction force from the scale R. The reading of scale is:
A
B
C
D
The apparent weight of a person in a lift moving downwards is half his apparent weight in the same lift moving upwards with the same magnitude of acceleration. Acceleration of the lift is:
A
B
C
D