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### 402-E: Block Dragging 1: Dragging a Block Without Friction

• Topic Cluster: Dynamics
• Topic: Quantitative Dynamics (Newton's Second Law)
• Objective: Given a block of a certain mass, draw a free-body diagram of the block when it is not moving or being pushed on a surfaced without friction; determine the net force and acceleration of the block.
• Content: Gravity, normal force, and applied force act on a block being dragged; by understanding these forces a physicist can understand the motion of the block.
• Level: 2

#### BACK to Ladder Quantitative Dynamics (Newton's Second Law)

In the previous section, we learned to calculate net force and acceleration. That calculation is the basis of dynamics, the science of explaining why things move the way they do. The next several sections on quantitative dynamics will follow a similar pattern: looking at a situation, drawing a quantitative free-body diagram of that situation, and using it to analyze that situation.

We will start with the simplest two free-body diagrams: a block at rest on a table, and a block being pulled on a frictionless table. These are certainly not the most exciting examples, but they give us a good opportunity to start using the methods and vocabulary of dynamics.

Crucial to this section is to understand how to use vectors. The forces on all of our free-body diagrams are vectors, meaning they have magnitude and direction, and none of our free-body diagrams are complete until we correctly know the magnitude and direction of every force!

#### Force 1: Gravity

Gravity is a force that attracts all mass to all other masses, but of course, here on earth, gravity is a force that always pulls you down. Sometimes, the force of gravity when here on earth is called the weight.

• On earth, the direction of gravity is always down.
• On earth, the magnitude of gravity is given by the formula $$F_g = m g$$.

$$F_g = mg$$

#### Force 2: Normal Force

• The direction of the normal force is always perpendicular to the surface. For these problems, the direction of normal force will be up.
• For now, the magnitude of the normal force will equal the magnitude of gravity. But know that in the future it will get much more complicated!
1. A block is resting on a table. It has a mass of 2 kg.
1. Fill out the table below to draw a complete free-body diagram of the block.
2. Use your free-body diagram to determine the net force $$\Sigma F$$ acting on the block.
3. Determine the acceleration $$a$$ of the block.
2. A block is resting on a table. It has a mass of 5 kg.
1. Fill out the table below to draw a complete free-body diagram of the block.
2. Use your free-body diagram to determine the net force $$\Sigma F$$ acting on the block.
3. Determine the acceleration $$a$$ of the block.

#### Force 3: Applied Force

An applied force is any force applied an on some object by a human. Common examples are pulls and pushes. The applied force is frequently a given value in a problem. That is, both magnitude an direction are often given in a problem.

1. An object with a mass of 2.00 kg is being pulled on a frictionless table. It is pulled with an applied force of 16.0 Newtons.
1. Fill out the table below to draw a complete free-body diagram of the block.
2. Use your free-body diagram to determine the net force $$\Sigma F$$ acting on the block.
3. Determine the magnitude of acceleration $$a$$ of the block. Please write formulas before using them.
2. An object with a mass of 3.56 kg is being pulled on a frictionless table. It is pulled with an applied force of 12.6 Newtons.
1. Fill out the table below to draw a complete free-body diagram of the block.
2. Use your free-body diagram to determine the net force $$\Sigma F$$ acting on the block.
3. Determine the acceleration $$a$$ of the block. Please write formulas before using them.