CHANGES IN FORCE AND MOTION

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1 reflect CRACK! That s the sound of a bat hitting a baseball. The ball fl ies through the air and lands over the fence for a home run. The motion of a batted ball seems simple enough. Yet, many forces act on the ball as it travels from home plate to the outfield. Why do some balls go further than others? Why do some balls move in an arc, soaring high into the sky and then dropping into the stands or a fielder s glove? Are all moving things affected by the same types of forces? Forces cause the energy of motion. When an object is at rest, its potential energy is at its greatest. When an object is in motion, potential energy is changing into kinetic energy. Energy changes from potential to kinetic when a force is applied. (A force is a push or pull.) One force is gravity, which pulls objects toward the center of Earth. For example, when a ball is held at the top of a tall tower, it has potential energy. When the ball is dropped, gravity pulls the ball toward the ground. As the ball falls, its potential energy changes to kinetic energy. All changes in motion require the input of a force. The simplest way to think about motion is a change in position. You ride your bicycle from your house to school. You have changed position through motion. The force of pedaling the bicycle causes this change. Forces can change motion in other ways, too. While riding your bike, you turn left at an intersection. You have changed direction. As you approach a stop sign, you slow to a stop and then speed up again. Speeding up and slowing down are also changes in motion caused by forces. The ball changes position as it falls from the top of the tower to the ground. Newton s first law of motion describes the effects of forces. Forces are measured in units called newtons (N). This unit is named for Sir Isaac Newton, a British scientist who identified and described three laws of motion. Newton s fi rst law of motion describes two important effects of forces: An object in motion stays in motion until an unbalanced force acts upon it. An object at rest (not moving) stays at rest until an unbalanced force acts upon it. 1

2 What exactly is an unbalanced force? When two equal forces are acting on an object from opposite directions, the forces are balanced. Look at the diagram below. The ball won t move in either direction. It stays at rest because the forces are balanced. Each person kicks the ball with a force of 50 N. The forces are equal, but they are applied in opposite directions. Therefore, the forces are balanced. The ball will not move. On the other hand, when forces are unbalanced the ball will move. The following diagrams show two different examples of unbalanced forces acting on a ball. The ball is kicked with a force of 50 N, so it will move in the direction of the kick. The greater the force, the farther the ball will move. The player on the left kicks the ball with a force of 25 N. The player on the right kicks the ball with a force of 100 N. In which direction will the ball move? Newton s fi rst law of motion also describes how forces affect objects already in motion. An object in motion will continue moving at the same speed and in the same direction until an unbalanced force acts upon it. This means if you kick a soccer ball straight across the ground, it should continue moving in a straight line, at the same speed, forever! However, you know this doesn t happen. The ball slows and eventually stops moving. A force must act on it as it moves. 2

3 look out! What force acts on the soccer ball to stop its motion? There are many possibilities. The soccer ball might run into a wall, which acts as a stopping force. It might be kicked by a friend whose foot acts as a force that changes the ball s direction and speed. But what force causes the ball to slow to a stop? The answer is a force called friction, which occurs between two surfaces that rub together in this case, the ball and the ground. Friction always acts in the opposite direction of motion. Slippery surfaces like ice have less friction than rough surfaces. An object in motion has speed. Speed describes rate of movement, or how fast something moves. Anything that moves across a distance over time has speed. It is calculated using the formula distance time: s = d t Scientists measure distances in units such as kilometers and meters. They measure time in units such as hours and seconds. Therefore, the most common units of speed are kilometers/hour (km/hr) and meters/ second (m/s). (The / is pronounced per. ) Suppose a fish swims 8 meters in 4 seconds. What is its speed? In other words, the fish swims 2 meters in 1 second, or 2 meters per second. Think back to the example of riding your bike to school. You probably pedaled faster at certain times and slower at others. You may even have stopped completely at a red light or stop sign. Although your speed is constantly changing as you move, you can calculate your average speed by dividing the total distance you traveled by the total time you took to get there: average speed total distance = total time So, let s say your school is 5 kilometers away, and you bike there in 15 minutes, or one-quarter (1/4 = 0.25) of an hour. Your average speed is 5 km 0.25 hr = 20 km/hr. At times during your trip you bike at a faster speed, and at times you bike at a slower speed; but your average speed is 20 km/hr. In other words, you would bike 20 kilometers in 1 hour, or 20 kilometers per hour. s = d t = 8 m 4s = 2 m/s 3

4 what do you think? Look at the map below. The red line shows the path that a person walked from home to school. The path contains fi ve different sections. The boxes in the map describe how long the person took to walk each section. What is the person s average speed? First, add the total distance the person traveled. Then add the total time of travel. Finally, divide the total distance by the total time. (The answer is at the end of the companion following the What do you know? section.) You can graph distance and time to show changes in motion. On a distance-time graph, time is always plotted on the horizontal x-axis. The distance that the object moves from a starting point is always plotted on the vertical y-axis. Each point of the graph is made by plotting the distance traveled at each given time. The distance-time graph on the next page shows three different kinds of motion. 4

5 Green line: A straight line like this means an object is moving at a constant speed. Object A is not speeding up, slowing down, or changing direction. You can calculate an object s speed by fi nding the slope of the line. The steeper the slope, the faster the speed. Red line: A line that changes directions like this means an object is changing speed or direction as it moves. Object B begins by moving 25 meters at a constant speed for 6 seconds. (The red line s slope is less steep than the green line s, so Object B is moving more slowly than Object A.) Between 6 seconds and 14 seconds the line is horizontal. This means Object B has stopped and is at rest. After 14 seconds, Object B moves 25 meters at a constant speed back toward its starting position. Here is how to calculate Object B s average speed. (Note that Object B moves a total distance of 50 meters.) average speed = total distance total time = 50 m 20 s = 5 m 2 s Blue line: A line that curves up like this means that an object is getting faster. Every second, Object C is moving a greater distance from its starting point. 5

6 What do you know? A horse gallops a distance of 60 meters in 15 seconds. Then, he stops to eat some grass for 20 seconds. Next, he trots for 25 seconds over 60 meters. (The horse trots in the same direction he galloped.) Finally, the horse races home (back to its starting position), traveling 120 meters in 20 seconds. Graph the horse s movements on the following distance-time chart. In the box below, calculate the horse s average speed for the entire journey. 6

7 what do you think? Remember earlier in this companion when you studied a map and calculated a person s average speed from home to school? Here is how to solve the problem. First, calculate total distance: 90 m m m m + 60 m = 640 m Next, calculate total time: 30 s + 60 s + 50 s + 40 s + 20 s = 200 s Finally, divide total distance by total time: 640 m 200 s = 3.2 m/s connecting with your child Daily Forces, Motion, and Speed To help students learn more about how a change in force affects motion, play a game of tug-of-war. This classic game shows students how balanced forces cancel out and cause no motion, while unbalanced forces cause movement. The game is played with at least two people. Tie a fl ag in the middle of a long rope. Then, each person (or half of a group of people) pulls on either end of the rope. When the forces are balanced, the fl ag does not move. When the forces are unbalanced, the flag moves toward the person or group pulling with the greatest force. Make sure to monitor the game so that students play safely remind groups not to pull so hard they risk injuring someone else. (It s best to talk students through the game. Begin with each side gently tugging on the rope, gradually adjusting the amount of force per side until the forces are balanced and the fl ag is at rest. Then, instruct one side to decrease the force with which it is pulling the rope, and watch how the flag moves in the direction of the greater force.) To practice calculating average speed, provide students with many opportunities to measure distance and time. For example, measure the distance and time of a trip to the grocery store, a walk to the park, a touchdown run on a football game, or a cross-court tennis shot. Have students take the measurements, and then calculate the average speed of each movement. Encourage students to manipulate the speed formula to find the different variables. For example, see if they can determine how long it will take to get to a destination if they know how far away it is and how quickly you travel. Suppose the grocery store is half a mile away about 2,500 feet and your child walks at an average speed of 200 feet per minute. To calculate the time it would take your child to walk to the grocery store, rewrite the speed formula to solve for time. Remember, the speed formula is usually written like this: average speed = total distance total time 7

8 To solve for total time, multiply both sides of the equation by total time and divide both sides by average speed: total time = total distance average speed = 2500 ft = 12.5 min 200 ft/min Your child could walk to the grocery store in about 12.5 minutes. You should also ask your students about the effects of unbalanced forces on objects. For example: Have you ever observed an unbalanced force change an object s position? (For example, what happens during a game of tug-of-war?) How do unbalanced forces affect the direction and speed of a soccer ball during a soccer game? Here are some questions to discuss with students: How do you know when forces on an object are balanced or unbalanced? How does speed differ from average speed? How would a quickly moving car look on a distance-time graph compared to a parked car? 8