Chapter 8 Motion and Forces Section 8.1 Motion
Motion We are surrounded by moving things. From a car moving in a straight line to a satellite traveling in a circle around the Earth, objects move in a variety of ways. Movement seems so common in our every day lives and may even appear to be a simple process. But understanding motion actually requires some new and advanced ideas. • Relate speed to distance and time. • Distinguish between speed and velocity Chapter 8 Objectives • Recognize that all moving objects have momentum. • Solve problems involving time, distance, velocity, and momentum
Speed and Velocity • Our every day experience shows that some objects move faster than others. Speed describes how fast and object moves. • Speed: the distance traveled by an object divided by the time interval during which the motion occurred.
Speed Measurements InvolveDistance and Time • To find speed you must take two measurements • Distance traveled by the object • The time it takes to travel that distance. • Speed is expressed as a distance unit divided by a time unit: • What is the unit for distance? • Meters m • What is the unit for time? • Seconds s • So what is the unit for speed? • Meters/ Seconds • m/s or said meters per second
Constant Speed • Constant Speed: when an object covers equal distances in equal amounts of time. • Example: A racecar traveling at a constant speed of 96 m/s will travel a distance of 96 meters each second.
Speed Can Be Determined By a Distance-Time Graph • We can investigate the relationship between speed, distance, and time by plotting a distance-time graph. • Objects moving with constant speed will be denoted by a straight line in which the slope of the line denotes the speed. • The steeper the line the faster the speed. • The line for speed three shows that the object is at rest. Why?
Speed is Calculated as DistanceDivided by Time • Most objects to do not move with constant speed. The speed of an object can change from one instant to another. • Because of this we use average speed: • Total distance covered/ total time it took to travel that distance • Speed Equation • Speed=v • Distance=d • Time=t
Example Problem • Suppose a wheelchair racer finishes a 132 m race in 18 seconds. Find the constant speed. • What are we looking for? • Speed (v)= ? • Knowns: • Distance (d)= 132 m • Time (t)= 18 s • So using the speed equation we get • v=d/t • Plug in known quantities • v= 132m/18s • v= 7.3 m/s
Velocity • Velocity: describes both speed and direction • Sometimes knowing the speed of an object is not enough. Sometimes we need to know the direction of travel. • For Example: • In 1997, a 200 kg lion escaped from a zoo in Florida. The lion was located by searchers in a helicopter. The helicopter crew was able to guide searchers on the ground by reporting the lion’s velocity (speed and direction of motion) • The escaped lion’s velocity may have been reported as 4.5 m/s to the north or 2.0 km/h toward the highway. • From this we can see that just knowing the lion was traveling 4.5 m/s is not enough information. We must know the direction in which it is traveling in order to find it.
Velocity • Velocity can be positive if moving in one direction or negative when moving in the opposite direction. • For this class we can assume that velocity will be positive in the direction of motion.
Velocity Example Problem • Metal stakes are sometimes placed in glaciers to help measure a glacier’s movement. For several days in 1936, Alaska’s Black Rapids glacier surged as swiftly as 89 m per day down the valley. Find the glacier’s velocity in meters per second. Remember, velocity includes the direction of motion. What do we want to know? Velocity (v)= ? What are the knowns? Distance (d)= 89 m Time (s)= 1 day Direction= down the valley What’s the problem here? We MUST convert days to seconds Knowns Distance (d)= 89 m Time (s)= 86,400 sec Direction= down the valley So using the speed equation we get v=d/t Plug in known quantities v= 89m/86,400 s v= 0.001 m/s Direction= down the valley Answer 0.001m/s down the valley
Momentum • Velocity and speed are not the only important quantities when objects are in motion. For example, a train is more difficult to stop than a car moving along the same path at the same speed. The train is more difficult to stop because it has a grater mass than the car. • Momentum takes the mass of the object into consideration. • Momentum: is a quantity defined as the product of an object’s mass and its velocity. • Momentum Equation: • p=mv • Momentum (p)= kg*m/s • Mass (m)= kg • Velocity (v)= m/s
Momentum Example Problem • Calculate the momentum of a 6.00 kg bowling ball moving at 10.0 m/s down the alley? • 1. What do we want to know? • Momentum (p)= ? • 2. What do we know? • Mass (m)= 6.00 kg • Velocity (v)= 10.0 m/s down the alley • 3. So using the speed equation we get • p=mv • 4. Plug in known quantities • p= (6.00 kg)(10.0 m/s) • 5. Answer • p= 60.0 kg*m/s Down the alley
Law of Conservation of Momentum • In the absence of outside influences, the total amount of momentum in a system is conserved. • If two cars of different masses and traveling with different velocities collide head on, you can use momentum to predict the motion of the cars after the collision. • The total momentum of the two cars before a collision is the same as the total momentum after the collision. The cars can bounce off each other to move in opposite directions, or they can stick together and continue in the direction of the car that originally had the greater momentum.