Density. Mass Volume. Density =

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Maurice Cory McDowell
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1 Mass Mass is a property of an object that measures how much matter is there in the object. It doesn t depend on where the object is. It doesn t have a direction.

2 Weight Weight is due to the gravitational attraction of the Earth. Weight is the (downward!) force on an object that is proportional to the mass. The unit of weight is the same as the unit of force Newton. On Earth surface, the weight of a 1kilogram mass is about 10 Newtons. Weight of an object can be different on different planets or stars. The gravitational attraction of Moon is only about 1/6 of that of Earth, so the weight of an object on Moon surface is only 1/6 of its weight on Earth. The mass of the object is the same. In outer space far from any stars or planets, there will be no gravitational attraction, so an object will have no weight but it has the same mass.

3 Density Density = Mass Volume 1. Density is a property of materials. 2. Given a sample, you can calculate its size (volume) from its mass if the density of the materials that make up the sample is known. 3. Given a sample, you can calculate its mass from its size (volume) if the density of the materials that make up the sample is known. 4. Be careful in units conversion. Units for volume: liter (=1000 cm 3 ), cm 3,m 3, in 3, ft 3, Units for mass: gram, kilogram,.

4 Constant speed x = 1cm 2cm 3cm 4cm 5cm 6cm 7cm 8cm O t = 1s 2s 3s 4s This picture shows the location of an object at successive times (1 second intervals). Note that in each second, the object moves 1 cm. Its speed is therefore 1 cm/s and is constant. In this example, an object is moving in a straight line, in one direction, with constant speed. You can calculate the speed of an object with constant velocity by taking any two points on the path and dividing the distance between them by the time duration between them. 5s 6s 7s 8s

5 Constant speed If an object is moving with a constant speed, its speed can be calculated as Speed = distance travelled time

6 Graph for constant speed x d (c cm) 10 In a graph of distance vs. time, 8 constant speed gives a straight 6 line: the steeper the line, the faster the 4 motion t (seconds) d = 1cm 2cm 3cm 4cm 5cm 6cm 7cm 8cm O t = 1s 2s 3s 4s 5s 6s 7s 8s

7 Graph for Uniform Motion x Which object is moving faster? In what directions are the objects moving? What is happening here? t Graph for constant speed is a straight line. Steepness or slope gives the speed of the Steepness or slope gives the speed of the motion.

8 Graph for Uniform Motion x Which object is moving faster? What is happening here? t Not moving is a particular case of uniform motion, with speed =0.

9 Graph for Non-uniform Motion - slowing down x Less steep (slower) More steep (faster) Object is moving away from the origin. t

10 Here s a graph for an object which is slowing down, but is moving toward ddecreasing values of x (e.g. toward the left). f) x More steep (faster) Object is moving towards the origin. Less steep (slower)

11 Non-uniform Motion speeding up x More steep (faster) Object is moving away from the origin. Less steep (slower)

12 Here s a graph for an object which is speeding up, but is moving toward decreasing values of x (e.g. toward the left). x Less steep (slower) Object is moving towards the origin. More steep (faster) t

13 Average speed If an object is not moving with a constant speed, we can calculate the average speed: Average speed = Total distance travelled Total time

14 Example As you can tell from the graph, Beth drove the first 40 miles at 60 mph, and then stopped for lunch, which took 20 minutes. But now she was going to be late, so she drove the rest of the way (35 miles) at 70 mph. What was her average speed for the trip? First part of Beth s trip: Distance travelled = 40 miles, Time = 40miles/60 mph = 2/3 hr = 40 minutes. Second part of Beth s trip (Lunch): Distance travelled = 0 miles, Time = 20 minutes. Third part of Beth s trip: Distance travelled = 35 miles, Time = 35miles/70 mph = 1/2hr = 30 minutes. Total distance = = 75 miles Total time = = 90 minutes Average speed = 75 /90 miles/min. = 5/6 miles/min = 5/6 60 mph = 50 mph

Example Total time = 90 minutes Total distance = 75 miles As you can tell from the graph, Beth drove the first 40 miles at 60 mph, and then stopped for lunch, which took 20 minutes.

15 Example Total time = 90 minutes Total distance = 75 miles As you can tell from the graph, Beth drove the first 40 miles at 60 mph, and then stopped for lunch, which took 20 minutes. But now she was going to be late, so she drove the rest of the way (35 miles) at 70 mph. What was her average speed for the trip? Alternatively, you can also calculate average speed as the slope of the straight line joining the two end points (red line) in the distance versus time graph. Average speed = slope of red line =(75-0) /(90-0) miles/min. = 5/6 miles/min = 5/6 60 mph = 50 mph

16 The Law of Inertia (Newton s First Law): In the absence of external forces, an object moves in a straight line with constant speed. 1. If you know there is no external force acting on an object, you know the object is moving in a straight line with constant speed. Note that at rest is a particular case of zero speed. 2. If you see an object not moving in a straight line with constant speed, you know there maust be external forces acting on it.

17 Example I A spaceship in outer space far from any yplanet or star, there will be no force acting on it. It will move with a constant speed. Does it need any fuel?

18 Example II You are driving a car and steering it around a curve. The car is not moving in a straight line, so there must be external lforce acting on the car (frictional force from ground by steering the wheels).

19 Example III Earth is revolving around Sun with a constant speed. The Earth is not moving in a straight line, so there must be an external force acting on the Earth (gravitational attraction from the Sun).

Force, Motion, and Sound

Force, Motion, and Sound Physics 160, Spring 2006 Galileo (1564-1642) 1642) Isaac Newton (1643-1727) 1727) Uniform Motion x = 1cm 2cm 3cm 4cm 5cm 6cm 7cm 8cm O t = 1s 2s 3s 4s 5s 6s 7s 8s This picture