## Drawing Free-Body Diagrams

5.7 Drawing Free-Body Diagrams

### Learning Objectives

By the end of this section, you will be able to:

- Explain the rules for drawing a free-body diagram
- Construct free-body diagrams for different situations

### Tactics for Drawing a Free-Body Diagram

**Identify all forces**acting on the object.**Draw a coordinate system**. Align one of the axes with the acceleration of the object.**Represent the object as a dot**at the origin of the coordinate axes. This is the particle model.**Draw vectors**representing each of the identified forces. Be sure to**label each force vector.****Draw and label the net force vector F**. Draw this vector beside the diagram, not on the particle. Then check that F_{net}_{net}points in the direction of the acceleration. Or, if appropriate, write F_{net }= 0.

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

When you apply an upward force of magnitude F to a block of mass 2.00 kg, the block accelerates upward at 3.00 m/s^{2}. You can ignore any forces exerted on the block by the air. Rank the following forces in order of their magnitude, from smallest to largest.

- the force F
- the net force on the block
- the gravitational force on the block

**Practice!**

Practice 5.7.1 |
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A block sits at rest on a frictionless surface. Each red arrow represents a force. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? |

(a) sketch A |

(b) sketch B |

(c) sketch C |

(d) sketch D |

(e) none of the above |

Practice 5.7.2 |
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Now, the same block moves with a constant velocity to the right on the frictionless surface. Which of the following most closely resembles the correct free body diagram for all forces acting on the block? |

(a) sketch A |

(b) sketch B |

(c) sketch C |

(d) sketch D |

(e) sketch E |

(f) none of these |

Practice 5.7.3 |
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Now, the block moves with a constant velocity to the right on a surface that has friction. Which of the following most closely resembles the correct free body diagram for all forces acting on the block? |

(a) sketch A |

(b) sketch B |

(c) sketch C |

(d) sketch D |

(e) none of these |

Practice 5.7.4 |
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Imagine standing in an elevator that is moving upward. Which of the following is the most complete list of the forces that belong on your Free-Body Diagram (FBD) in that moment? |

(a) The normal force on you by the elevator floor and the force of gravity on you by the earth |

(b) The normal force on you by the elevator floor, the force of gravity on you by the earth, and the force of acceleration on you by the motor |

(c) The force of gravity on you by the earth and the force of acceleration on you by the motor |

(d) The force of gravity by the earth on you and the force of you on the elevator floor |

Practice 5.7.5 |
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Imagine a car sitting empty in the parking lot. Which of the following is the most complete list of the forces that belong on a Free-Body Diagram (FBD) of the car? |

(a) The force on your car by its engine and the force of you pushing down on your car |

(b) The normal force of your car on the pavement it rests on and the force of gravity pulling on the earth |

(c) The normal force on your car by the pavement it rests on and the force of gravity on your car by the earth |

(d) The force on your car by you and the force of your car on the air around it |

Practice 5.7.6 |
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An object rests on a ramp that is angled at 20° above the horizontal. What direction (relative to the vertical) will the normal force from the ramp point? |

(a) The normal force will be directed at 70° away from the vertical. |

(b) The normal force will be directed at 20° away from the vertical. |

(c) The normal force will be directed exactly upward, along the vertical. |

(d) The normal force will be directed horizontally, 90° away from the vertical. |