You are standing in a city bus, not holding the rail. The driver brakes hard. You lurch forward, and you have to grab a rail or a seat. When the bus starts again with a jerk, you fall backward. It feels as if a force pushed you forward in the first case and backward in the second.
The old idea: motion needs a push
Push a book along a table and let go. The book slows down and stops. Stop pedalling a bicycle and it soon comes to rest. Everyday experience suggests that a body moves only while something pushes it. For about two thousand years, following Aristotle, this was the accepted view. It is wrong, and finding out why it is wrong is the start of mechanics.
Galileo's two ramps
Galileo let a ball roll down one smooth ramp and up a second ramp facing it. The ball climbed the second ramp to almost the height it started from. The smoother the ramps, the closer it came to the starting height. Then Galileo made the second ramp less steep. The ball still climbed to the same height, but it had to travel farther along the ramp to get there.
The second ramp is made flat, so it never rises at all. There is no friction. What does the ball do after it reaches the flat part?
Step through the three states of Fig 2.1. On the steep second ramp the ball stops after a short climb. On the gentle ramp it travels much farther before stopping at the same height. On the flat track the ball can never regain its height, so it rolls on at a constant speed. Galileo concluded that a moving body keeps moving unless something acts to stop it.
Why things stop
The book on the table stops because the table exerts friction on it. The bicycle stops because of friction at the axles and the push of the air. Remove these forces and the motion goes on. So the question to ask is never "what keeps it moving?". The right question is "what force stops it, or turns it?".
Look at the dots in Fig 2.2. On concrete the gaps between the dots shrink quickly, because the friction force is large. On tiles they shrink slowly. On ideal ice the gaps never change. Equal gaps in equal times mean constant velocity. The smaller the force, the smaller the change in velocity, and with no force there is no change at all.
A hockey puck slides on perfectly smooth ice with no air resistance. What is needed to keep it moving at \(5\,\text{m/s}\)?
Inertia
A body resists any change in its state of rest or of uniform motion. This property is called inertia. A body at rest stays at rest. A body in motion keeps the same speed in the same direction. Inertia is not a force. It is the tendency of a body to keep its velocity, whatever that velocity is.
The first law
Newton put Galileo's idea at the top of his laws of motion. One more word is needed. Several forces may act on a body at once, and they may cancel. What matters is their vector sum, the net force \(\sum \vec F\). A body with forces that cancel behaves exactly like a body with no force at all. The net force is the only force the first law cares about.
A body remains at rest, or moves with constant velocity in a straight line, unless a net external force acts on it.
The first law says two things. First, zero net force means zero acceleration: the velocity is constant, and rest is simply the case \(\vec v = 0\). Second, any change in velocity, in speed or in direction, tells you that a net force acts. A car turning a corner at a steady \(40\,\text{km/h}\) has a changing velocity, so a net force acts on it, even though its speed is constant.
A Metro train moves along a straight track at a constant \(72\,\text{km/h}\). What is the net force on the train?
In which of these situations is the net force on the body zero? Choose all that apply.
Paying off the bus
Return to the bus. Before the brakes act, you and the bus move forward together. The brakes exert a force on the bus, so the bus slows down. Nothing pushes your body backward with the bus, because you are not holding anything. By inertia your body keeps moving forward at the old speed. The bus slows under you, so you move forward relative to the bus. No force pushed you forward; the bus was pulled back from under you.
Where the law holds
The first law does not hold in every frame of reference. Watch a ball on the floor of the braking bus. It rolls forward, although no horizontal force acts on it. An observer in the bus sees a velocity change with no force. An observer on the road sees the ball simply keep its velocity while the bus slows. A frame in which the first law holds is an inertial frame. The road is one; the braking bus is not.
A frame fixed to the ground is inertial to a very good approximation. The Earth's own spin and its orbit make it accelerate very slightly, but for every problem in this book the ground is an inertial frame. Solve problems from the ground unless a question says otherwise.
A bus moving at \(36\,\text{km/h}\) brakes to rest in \(2\,\text{s}\). A passenger is not holding anything. Roughly how far forward, relative to the bus, does the passenger's body try to move during the braking? Give metres.
Galileo described his two ramps in Dialogues Concerning Two New Sciences, published in 1638. He noticed that a ball rolling on a level track would have no reason to speed up and no reason to slow down. He concluded that its motion would be perpetual, if the track were long enough and smooth enough. Newton was born in the same year that Galileo died, 1642. Forty-five years later, Newton's first law stated Galileo's idea for every body.
In a car crash the car stops in a fraction of a second. By inertia the passengers keep moving forward at the car's old speed. Without a belt they move until the dashboard or the windscreen stops them. A seat belt exerts a force on the passenger's body over a longer time, which stops the body together with the car. The headrest does the same job in a crash from behind, stopping the head from staying back while the car and the body lurch forward.
- Believing that a moving body needs a force to keep it moving.Motion needs no force. A force is needed only to change the velocity.
- Saying that inertia is a force that pushes the passenger forward.Inertia is a property, not a force. The passenger keeps moving; the bus is what changes.
- Thinking that constant speed on a curve means zero net force.A change of direction is a change of velocity, so a net force acts.