2. Class 10 - Force and Motion I Chapter 5 - Wednesday September 16th Force and acceleration Newton's first law Force and mass Newton's second law Some particular forces Reading: pages 87 thru 99 (chapter 5) in HRW Read and understand the sample problems Assigned problems from chapter 5: 24, 26, 34, 38, 44, 46, 52, 56 (due Sun. Sept. 26) 24, 26, 34, 38, 44, 46, 52, 56 (due Sun. Sept. 26)

3. What causes acceleration? Linguistic arguments: Some sort of interaction - loosely speaking, a push or a pull on an object.Some sort of interaction - loosely speaking, a push or a pull on an object. We call this a force, which can be said to act on a body.We call this a force, which can be said to act on a body. Examples of forces:Examples of forces: Normal or "contact force" Gravitational force Electromagnetic force Weak and strong nuclear forces

4. We'd better be more scientific about this...

5. Before Newton Friction and air resistance have a tendency to distort our appreciation of the nature of forces.Friction and air resistance have a tendency to distort our appreciation of the nature of forces. Think of a motor boat or a car: their engines constantly do work (i.e. generate driving forces) in order to maintain a constant velocity.Think of a motor boat or a car: their engines constantly do work (i.e. generate driving forces) in order to maintain a constant velocity. This led people to believe, before Newton, that a force was necessary to keep a body moving at constant velocity, and that the natural state of a body was when it was stationary - this leads to some very interesting philosophical questions.This led people to believe, before Newton, that a force was necessary to keep a body moving at constant velocity, and that the natural state of a body was when it was stationary - this leads to some very interesting philosophical questions. But hang on a minute.... What happens if we remove all resistance to motion, i.e. friction and air resistance?

6. Newton's first law If no force acts on a body, then the body's velocity cannot change; that is, it cannot accelerate. An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Therefore, according to Newton, the car traveling at constant velocity experiences no net or unbalanced force.Therefore, according to Newton, the car traveling at constant velocity experiences no net or unbalanced force. That is, the engine forces it one way, and friction exactly balances this force by opposing the motion with an equal and opposite force.That is, the engine forces it one way, and friction exactly balances this force by opposing the motion with an equal and opposite force. Friction is a somewhat mysterious force, though we will learn to deal with it in the next chapter.Friction is a somewhat mysterious force, though we will learn to deal with it in the next chapter.

7. Force We declare that: a force of 1 Newton is that force required to accelerate our standardized mass (1 Kg) at a rate of 1 m.s -2.We declare that: a force of 1 Newton is that force required to accelerate our standardized mass (1 Kg) at a rate of 1 m.s -2. A reference defines the Kg, and the above definition defines force.A reference defines the Kg, and the above definition defines force. Definition (there is no proof!): Force is a vector. Thus, forces add like vectors. This is something one has to test by experiment.Force is a vector. Thus, forces add like vectors. This is something one has to test by experiment. Forces obey the "principle of superposition.“Forces obey the "principle of superposition.“

8. Free-body diagrams The forces shown above are what we call "external forces."The forces shown above are what we call "external forces." They act on the "system" S.They act on the "system" S. S may represent a single object, or a system of rigidly connected objects. We do not include the internal forces which make the system rigid in our free body diagram.S may represent a single object, or a system of rigidly connected objects. We do not include the internal forces which make the system rigid in our free body diagram.

9. Inertial reference frames An inertial reference frame is one in which Newton's laws hold. Simply put: this is a frame which is not accelerating. *Assuming we define mass in the same way in all inertial frames Newton's laws do not apply in accelerating frames.Newton's laws do not apply in accelerating frames. They must also be modified in relativistic and quantum limitsThey must also be modified in relativistic and quantum limits

10. What is mass? On earth, we use the fact that the acceleration due to gravity is approximately constant for all objects, and characterize an “effective” mass according to the force needed to balance the earth's gravitational force.On earth, we use the fact that the acceleration due to gravity is approximately constant for all objects, and characterize an “effective” mass according to the force needed to balance the earth's gravitational force. We call this "weight", as measured in Newtons (v. imp!)We call this "weight", as measured in Newtons (v. imp!) In outer space, everything is weightless, but not massless!!In outer space, everything is weightless, but not massless!! This is not a trivial question! Mass is simply the characteristic of a body that relates a force on the body to the resulting acceleration This is how one has to measure mass in outer space.This is how one has to measure mass in outer space. No static method works, because there is no basis for comparison, e.g. hanging or spring balances, which depend on g.No static method works, because there is no basis for comparison, e.g. hanging or spring balances, which depend on g. YOUR MASS DOES NOT CHANGE IN OUTER SPACE!!!YOUR MASS DOES NOT CHANGE IN OUTER SPACE!!!

11. Newton's second law This law was developed through systematic experimentation 1) We calibrate our force apparatus by accelerating our standard mass by 1, 2, 3, etc.. m.s -2. 2) We then apply a standard force of 1 N to a range of objects, and measure their acceleration. 3) We then look for the relationship between force, mass and acceleration. And the result: We may treat the components separately.We may treat the components separately. Mass is a scalar quantity.Mass is a scalar quantity. 1 N = (1 Kg)(1 m.s -2 ) = 1 Kg.m.s -21 N = (1 Kg)(1 m.s -2 ) = 1 Kg.m.s -2

12. Some particular forces During free fallDuring free fall Gravity: This is always true at the surface of the earth, and will usually be the case for problems worked in this class.This is always true at the surface of the earth, and will usually be the case for problems worked in this class. In other words, even when a mass is stationary on the surface of a table, gravity still acts downwards with a magnitude equal to mg.In other words, even when a mass is stationary on the surface of a table, gravity still acts downwards with a magnitude equal to mg. This leads to the concept of a normal force: for the mass on the table to remain stationary, the table must exert an upward force on the mass so as to exactly balance the force due to gravity.This leads to the concept of a normal force: for the mass on the table to remain stationary, the table must exert an upward force on the mass so as to exactly balance the force due to gravity.

13. Normal force Weight (a force!): In the above example, the internal forces within the table supply the normal force.In the above example, the internal forces within the table supply the normal force. If we hold the mass in a stationary state, we must supply the force. This is the sensation of weight, i.e.If we hold the mass in a stationary state, we must supply the force. This is the sensation of weight, i.e.