Students Should Understand the Sum of Forces, F and Fnet

PPT Equilibrium

Developer Notes .

Version Date Who Revisions 05 2003/12/02 dk . Added revision table and re-formatted . Expanded goals . Added student reading . Added more exercises . Expanded teacher section 06 2004/06/22 Sc . Added note about drawing vector diagrams for activity . Eliminated normal force . Eliminated reference to projectiles . Added answers to exercises 07 2004/06/30 dk . Added section on velocity and acceleration 08 2004/08/05 dk . Updated from summer workshop . Added vector diagrams to activity

Goals . Students should understand the sum of forces, ∑F and Fnet. . Students should understand that the sum of forces can be zero or non-zero. . Students should know that if the sum of forces is zero, the object is in equilibrium. . Students should know that if an object is not moving, the sum of forces is zero, and the object is in equilibrium. . Students should know that if the sum of forces is non-zero, the object will accelerate. . Students should know that an object can be moving and still be in equilibrium. This is true if the object is moving at a constant velocity.

Concepts & Skills Introduced

Area Concept physics equilibrium, Fnet = 0, ∑F=0

Time Required

Warm-up Question Place a bowling ball on the floor: Write about the forces on the ball and its motion. Draw a vector diagram of the forces acting on the ball.

Presentation Discuss the warm-up question. The point is that there are forces on the ball, but the ball isn't moving because all the forces equal out. Gravity is pulling down on the ball, but the floor is pushing up. Air might be blowing on the ball, but friction is pushing back. The ball is in equilibrium. In mathematical notation: . Fnet = 0, the net force is zero, or . ∑F = 0, the sum of forces is zero.

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If the forces on the ball didn't equal out, then the ball would start moving. For moving objects, the same holds true; if the forces on the object don't equal out, the object will speed up, slow down, or turn.

This is a re-statement of Newton’s 1st Law of Motion. Objects remain in equilibrium unless an outside force acts on them.

It is very important here that the students understand the equivalence of non-zero net force and acceleration (or ∆v). ∑F, a, and ∆ are always either all zero or all non-zero.

∑F (Fnet) a ∆v = 0 = 0 = 0  0  0  0

For the activity, drawing vector diagrams of each situation helps. You may want to encourage the students to do this or observe how many students automatically do this.

Assessment

Writing Prompts 1.

Relevance

Summary

Answers to Exercises 1. a. 0, b. 0, c. 0, d. 0, e. 0, f. 0 2. non-zero, zero 3. non-zero, zero 4. Depends if the sled is moving at a constant velocity or not. If the speed and direction aren’t changing, the net force is zero. 5. no 6. yes 7. it’s non-zero 8. zero

Answers to Challenge/ extension 1.

Background We know that force causes acceleration. What happens when you combine forces?

Problem If an object is not moving, does that mean there are no forces acting on it? If an object is moving, does that mean there is an overall force acting on it?

Materials 2 spring scales, calibrated 1 paper clip 1 mass cart 1 electric car

Procedure 1. Hook both spring scales to the paper clip. a. Pull the two scales a little way apart and record the readings on the scales. b. Pull the scales a little further apart and record the readings on the scales. c. Draw a vector diagram of the forces on the paper clip. 2. Roll the cart across the floor. a. Does the cart speed up, slow down, or go at a steady speed? b. What are the forces on the cart as it rolls across the floor? c. Draw a vector diagram of the forces on the cart. 3. Run the electric car across the floor. a. Does the car speed up, slow down, or go at a steady speed? b. What are the forces on the car as it rolls across the floor? c. Draw a vector diagram of the forces on the car.

Summary 1. What is the sum of forces on the paper clip? 2. Is the sum of forces on the cart is zero or non-zero? 3. Is the sum of forces on the electric car is zero or non-zero? 4. Look at your data from the friction activity, where you were pulling the backpack at steady speed. Do you think the sum of forces on the backpack was zero or non-zero? 5. Can you make a general rule from the data you've found here? (Think about inertia.)

Reading What is the sum of all the forces on a moving object?

An object sitting still (relative to what?) has forces acting on it, like gravity and the force of the table or floor, but it isn't moving. All the forces on it equal out. Gravity may be pulling it down, but the floor is pushing it up an equal amount. Wind may be blowing on it, but there's an equal amount of friction. It is in equilibrium. Equilibrium means that the total (sum, net) of all the forces acting on it is zero. If the total wasn't zero, it would start moving. That's what Newton's 1st Law says.

How about an object that is moving? Can it be in equilibrium? By Newton's 1st Law, if the object is going in a straight line at a constant speed, there must be no net force on it, or else it would speed up, slow down, or turn. For a car going at a steady speed on a straight highway, the force of the tires pushing it forward is exactly matched by friction and air resistance, so it doesn't speed up or slow down. The car is in equilibrium.

Imagine a hockey puck sliding across frictionless ice in a straight line at a steady speed. There is no force pushing it, and there is no friction resisting it. The hockey puck is in equilibrium.

For an object that's in equilibrium, the sum of forces is zero. This can be written in symbols: . ∑F = 0. The sum of forces is zero. (∑ means "sum of.”) . Fnet = 0. The net force is zero.

Objects remain in equilibrium unless an outside force acts on them.

The total force on an object can be zero or non-zero. If it is zero, the object is in equilibrium whether it is moving or not. If it is non-zero, the object will change velocity (accelerate). Likewise, if an object goes at a constant velocity (no acceleration), the sum of forces on it must be zero.

Exercises 1. A box is sitting on a floor, not moving. a. What is the net force on the box? b. You push on the box as hard as you can, but it doesn’t move. What is the net force on the box? c. You climb on top of the box in frustration and sit down. What is the net force on the box? d. You get a friend to help you push the box, and you finally get it moving, slowly at first, then a little faster. What is the net force on the box while it is speeding up? e. Eventually you reach a constant velocity. What is the net force on the box? f. You reach your destination and quit pushing. The box slides to a stop. What is the net force on the box while it is slowing down? 2. When a rocket is taking off, is the net force on it zero or non-zero? What is the net force on a rocket coasting through deep space with its engines off? (Deep space means far away from any planets or stars, where the universe is essentially empty and gravity pulls equally in all directions.)

3. When an airplane is taking off, is the net force on it zero or non-zero? If the airplane has its engine running, and it is flying at a constant velocity of 200 kph, what is the net force on it? 4. In football, coaches make the players run into a blocking sled and push it. When the players are pushing the sled as fast as they can, what is the net force on the sled? 5. If an object is moving, does that mean it's can’t be in equilibrium? 6. When something is balanced, like a Chinese acrobat on a stack of chairs, could we say they are in equilibrium? 7. If a car is speeding up from a stoplight, what can you say about the net force on it? 8. If an object has a constant velocity, what can you say about the net force on it?

Challenge/ extension 1. Politically, what does it mean when we are in equilibrium?

Glossary . Equilibrium – a state of balance, when the total force on an object is zero. This can be written as Fnet = 0 or ∑F = 0.

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