## Newton’s Second Law

5.3 Newton’s Second Law

### Learning Objectives

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

- Distinguish between external and internal forces
- Describe Newton’s second law of motion
- Explain the dependence of acceleration on net force and mass

### Newton’s Second Law

**Practice!**

Practice 5.3.1 |
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A constant force is exerted on a cart that is initially at rest on an air track. Friction between the cart and the track is negligible. The force acts for a short time interval and gives the cart a certain final speed. To reach the same final speed with a force that is only half as big, the force must be exerted on the cart for a time interval ________ as long as that for the stronger force. |

(a) 4 times |

(b) 2 times |

(c) equal to |

(d) 1/2 |

(e) 1/4 |

Practice 5.3.2 |
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A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. The same force is exerted for the same length of time on another cart, also initially at rest, that has twice the mass of the first one. The final speed of the heavier cart is ________ times that of the lighter cart. |

(a) 1/4 |

(b) 4 |

(c) 1/2 |

(d) 2 |

(e) 1 |

Pause and Predict 5.3.1 |
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A 1000-N elevator is suspended by a cable. As the elevator is moving downward, it slows down at a rate of 3 m/s^{2}. What is the tension in the cable while the elevator slows down? |

(a) 1000 N |

(b) 1100 N |

(c) 1200 N |

(d) 1300 N |

(e) 1400 N |

Pause and Predict 5.3.2 |
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You pull on the block with 3 N of force at an angle of 34° above the horizontal and then your friend pulls on the same block in the opposite direction, parallel to the table. With how much tension should your friend pull on the block so that the block slides to the right at a constant speed? |

(a) 1.7 N |

(b) 2.5 N |

(c) 3 N |

(d) 3.3 N |

(e) 0 N |

**Practice!**

Practice 5.3.3 |
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With your hand parallel to the floor and your palm upright, you raise a 3-kg book upward with an acceleration of 2 m/s^{2}. What is the magnitude of force that your hand exerts on the book while it is accelerating? |

(a) 35 N |

(b) 23 N |

(c) 29 N |

(d) 6 N |

Practice 5.3.4 |
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With your hand parallel to the floor and your palm upright, you lower a 3-kg book downward. If the force exerted on the book by your hand is 20 N, what is the book’s acceleration? |

(a) 16 m/s^{2} downward |

(b) 16 m/s^{2} upward |

(c) 9.8 m/s^{2} downward |

(d) 9.8 m/s^{2} upward |

(e) 6.7 m/s^{2} downward |

(f) 6.7 m/s^{2} upward |

(g) 3 m/s^{2} downward |

(h) 3 m/s^{2} upward |

Practice 5.3.5 |
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You push a shopping cart filled with groceries (total mass = 20 kg) by applying a force to the cart 30° from the horizontal. If the force you apply has a magnitude of 86 N, what is the cart’s acceleration? Assume negligible friction. |

(a) 4.3 m/s^{2} |

(b) 3.7 m/s^{2} |

(c) 2.2 m/s^{2} |

(d) 5.5 m/s^{2} |

**Discuss!**

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

A .22 caliber rifle bullet travelling at 350 m/s strikes a large tree and penetrates it to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume a constant force from the tree acts on the bullet to slow it down and bring it to a stop.

(a) How much time is required for the bullet to stop?

(b) What force, in newtons, does the tree exert on the bullet?