## Friction

6.2 Friction

### Learning Objectives

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

- Describe the general characteristics of friction
- List the various types of friction
- Calculate the magnitude of static and kinetic friction, and use these in problems involving Newton’s laws of motion

### Friction

**Discuss!**

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

### At-home experiment to determine the coefficient of static friction

The coefficient of static friction between two objects is determined experimentally. Below is a table that gives some friction coefficients for different materials:

To experimentally determine the coefficient of static friction between two objects, you will need the following materials:

- ruler or meter stick
- flat, somewhat rigid, and movable surface, like a book or a piece of cardboard
- some object that can slide on the flat surface

Place the flat surface on a table and place the object on the flat surface. When you lift one end of the flat surface, it makes an angle θ with the table. If you increase this angle enough, the object on it will slide down. You want to find the angle where the object is *just about to slide* but not actually sliding. This is the point of impending slip and where the static frictional force is a maximum. If you increase the angle any more, the object slides and the frictional force becomes kinetic friction.

With the flat surface at this maximum angle and the object not sliding (but is at the point of impending slip), measure the angle. You can use the meter stick to measure two sides of the right triangle formed with the flat surface and the table. Then use the necessary trig to find the angle.

Draw a free body diagram of the forces acting on the object when it is at this point of impending slip. Then use the free body diagram and Newton’s 2nd law to solve for μ. This will be a function of the angle. Plug in the value of the angle you measured to find a numerical value for the coefficient of static friction.

Consider a box that is placed on different surfaces. In which situation(s) is no friction forces acting on the box? In which situation(s) is a static friction force acting on the box? In which situation(s) is a kinetic force acting on the block?

- The box is at rest on a rough horizontal surface.
- The box is at rest on a rough tilted surface.
- The box is on the rough-surfaced flat bed of a truck that is moving at a constant velocity on a straight level road, and the box remains in place in the middle of the truck bed.
- The box is on the rough-surfaced flat bed of a truck that is speeding up on a straight level road, and the box remains in place in the middle of the truck bed.
- The box is on the rough-surfaced flat bed of a truck that is climbing a hill, and the box is sliding toward the back of the truck.

**Practice!**

Practice 6.2.1 |
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You are walking on a level floor. You are getting good traction, so the soles of your shoes don’t slip on the floor. Which of the following forces should be included in a free-body diagram for your body? |

(a) the force of kinetic friction that the floor exerts on your shoes |

(b) the force of static friction that the floor exerts on your shoes |

(c) the force of kinetic friction that your shoes exert on the floor |

(d) the force of static friction that your shoes exert on the floor |

(e) more than one of these choices |

Practice 6.2.2 |
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A car of mass M is moving on a highway. The driver applies the brakes and the car starts to slide. Assuming a coefficient of kinetic friction μ _{k}, what is the car’s acceleration? |

(a) μ_{k}M |

(b) μ_{k}g |

(c) Mg |

(d) μ_{k}Mg |

(e) Not enough information to determine |

Practice 6.2.3 |
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Two vehicles of mass M and 2M are moving in the same direction on a highway. Both drivers apply their brakes at the same time and both vehicles begin sliding. If the coefficient of kinetic friction μ _{k} is the same for both vehicles, how do their accelerations a_{1} and a_{2} compare? |

(a) a_{1} is twice a_{2} |

(b) a_{1} is the same as a_{2} |

(c) a_{1} is half a_{2} |

(d) Not enough information to determine |

Practice 6.2.4 |
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Consider a car sitting parked on level ground. The force of friction between a car tire and the ground |

(a) is zero. |

(b) points forward (the direction the car is facing). |

(c) points backward (opposite the direction the car is facing). |

(d) points upward (perpendicular to the ground). |

Practice 6.2.5 |
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You are laying on your back on the slope of a grassy hill, watching the clouds go by overhead. Which is the best statement about the force of friction exerted on you by the ground in this situation? |

(a) A force of kinetic friction pointing “up the hill”, parallel to the surface of the hill, is applied to you by the ground. |

(b) A force of static friction pointing “up the hill”, parallel to the surface of the hill, is applied to you by the ground. |

(c) A force of static friction pointing upward, perpendicular to the surface of the hill, is applied to you by the ground. |

(d) A force of kinetic friction pointing upward, perpendicular to the surface of the hill, is applied to you by the ground. |

(e) No force of friction is applied to you by the ground. |

Practice 6.2.6 |
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You are about to check out at the grocery store and you put a box of cereal on the conveyer belt at the register. What is true about the frictional force acting on the box of cereal as it moves with the conveyer belt toward the cashier? |

(a) There is a kinetic frictional force pointing opposite to the box’s direction of motion, parallel to the conveyer belt. |

(b) There is a static frictional force pointing opposite to the box’s direction of motion, parallel to the conveyer belt. |

(c) There is a kinetic frictional force pointing in the box’s direction of motion, parallel to the conveyer belt. |

(d) There is a static frictional force pointing in the box’s direction of motion, parallel to the conveyer belt. |