Download Dr. Kauffman: Physics 26 Sept 2011 Newton`s Laws of Motion

Dr. Kauffman: Physics 26 Sept 2011
Newton’s Laws of Motion
Newton’s Laws of Motion:
1. An object at rest tends to stay at rest and an object in motion tends to stay in constant motion UNLESS
acted upon by a net outside force.
 Also called Newton’s Law of Inertia
 An objects velocity does not change if and only if the net force acting on the object is zero
 No force is required to keep an object in motion if there are no forces opposing its motion
 In the absence of friction and other resistive forces, no continued force is needed to keep an object
moving (Galileo). In such a case, the object would move in a straight line (Descrates). Newton built
upon this work, stating “If I have seen further, it is because I was standing on the shoulders of giants.”
 Try this at home: place a quarter on top of a credit card balanced on top of a drinking glass. With your
thumb and forefinger, flick the card so it flies out horizontally from under the quarter. What happens to
the quarter?
 Translational equilibrium: all forces acting on an object are balanced out (there is as much force acting
up as down an as much force acting to the left as to the right). We use free body diagrams to analyze the
forces acting on an object.
2. A force acting upon an object is given as the product of the mass of the object and its acceleration.
∆𝒗
𝑑𝒗
 𝑭 = 𝑚𝒂 = 𝑚
= 𝑚 where F is the force vector, m is the mass of the object, a is the
∆𝑡
𝑑𝑡
acceleration vector defined as the change in the velocity vector with respect to time
3. For every action (force), there is an equal and opposite reaction (force). If object A pushes on object B with
a force F, then object B pushes on object A with a force equal to F but acting in the opposite direction.
 These two equal but opposite forces are called an interaction pair.
 The forces must be acting on two DIFFERENT objects. For example, two children pulling on a toy in
opposite directions are not an example of Newton’s Third Law. Both forces are acting on the toy.
However, the force of the toy acting on the first child is equal and opposite to the force of the first child
acting on the toy.
 These forces must be between interaction partners.
 In an interaction between two objects, each object exerts a force on the other. These two forces are
equal in magnitude but opposite in direction.
4. Newton’s Law of Universal Gravitation: there is a force of attraction between any object with mass m1 and
any other object with mass m2. The strength of that force is directly proportional to the product of the
masses of the two objects and inversely proportional to the square of the distance between them, r. The
constant of proportionality is called the universal gravitational constant.
𝐺𝑚1 𝑚2
 Mathematically, this is written as: 𝐹 =
𝑟2
 The force always acts to pull the two objects towards each other
 When the distance separating the two objects is the radius of Earth and m1 is the mass of Earth, this
force is defined as the weight of an object.
𝐹𝑤 = 𝑤 =
𝐺𝑚𝐸𝑎𝑟𝑡ℎ 𝑚
N
m
=
𝑚𝑔
=
9.8
[
]
𝑚
=
9.8
[
]𝑚
2
kg
s2
𝑟𝐸𝑎𝑟𝑡ℎ
Conceptual Questions:
1. Explain the need for automobile seat belts in terms of Newton’s First Law.
2. You are lying on a beach where the waves are buffeting you around. Is it true that there are now no
forces acting on you? Explain.
3. When a car begins to move forward, what force makes it do so? Remember that it has to be an external
force, the internal forces all add to zero. How does the engine facilitate the propelling force?
4. A freight train consists of an engine and several identical cars on level ground. Determine whether each
of these statements is correct or incorrect and explain why. (a) If the train is moving at constant speed,
the engine must be pulling with a force greater than the train’s weight. (b) If the train is moving at
constant speed, the engine’s pull on the first car must exceed that car’s backward pull on the engine. (c)
If the train is coasting, its inertia makes it slow down and eventually stop.
5. What is the distinction between a vector and a scalar quantity? Give two examples of each.
Dr. Kauffman: Physics 26 Sept 2011
Newton’s Laws of Motion
6. If a wagon starts at rest and pulls back on you with a force equal to the force with which you pull on it,
how is it possible for you to make the wagon start to move? Explain.
7. A passenger sitting in the rear of a bus claims that he was injured when the driver slammed on the
breaks, causing a suitcase to come flying towards the passenger from the front of the bus. If you were
on the jury in this case, which way would you decide? Why?
8. In a tug-of-war between two athletes, each athlete pulls on the rope with a force of 200 N. What is the
tension in the rope? What force(s) does each athlete exert on the ground (magnitude, direction,
source).
9. If you push on a heavy box which is at rest, it requires some force F to start its motion. However, once it
is sliding, it requires a smaller force to maintain that motion. What is this so?
10. Is it possible to have motion in the absence of force(s)? Explain.
Multiple Choice Questions:
1. Interaction partners
a. are equal in magnitude and opposite in direction and act on the same object.
b. are equal in magnitude and opposite in direction and act on different objects.
c. appear in a free-body diagram for a given object.
d. always involve gravitational force as one partner.
e. act in the same direction on the same object.
2. Within a given system, the internal forces
a. are always balanced by the external forces.
b. all add to zero.
c. are determined only by subtracting the external forces from the net force on the system.
d. determine the motion of the system.
e. can never add to zero.
3. A friction force is
a. a contact force that acts parallel to the con tact surface.
b. a contact force that acts perpendicular to the contact surface.
c. a scalar quantity since it can act in any direction along a surface.
d. always proportional to the weight of an object.
e. always equal to the normal force between the objects.
Short Problems:
1. A person weights 120 lbs. Determine (a) her weight in N and (b) her mass in kg.
2. On planet X, an object weighs 10 N. On planet B, where the acceleration due to gravity is 1.6g, the object
weighs 27 N. (a) What is the weight of the object on Earth? (b) What is the mass of the object? (c) What
is the acceleration due to gravity (in m/s2) on planet X?
3. A force, F, applied to an object of mass m1 produces an acceleration of 3 m/s2. The same force applied to
a second object of mass m2 produces an acceleration of 1 m/s2. (a) What is the value of the ratio m1/m2?
(b) If m1 and m2 are combined, find their acceleration under the action of the force F.
4. A constant force changes the speed of an 80 kg sprinter from 3 m/s to 4 m/s in 0.5 s. (a) Calculate the
magnitude of the acceleration of the sprinter. (b) Obtain the magnitude of the force. (c) Determine the
magnitude of the acceleration of a 50 kg sprinter experiencing the same force. (assume linear motion).
5. What is the mass of an astronaut whose weight on the moon is 115 N? The acceleration due to gravity
on the moon is 1.63 m/s2.
6. If a man weighs 900 N on earth, what would he weigh on Jupiter, where the acceleration due to gravity
is 25.9 m/s2?
7. Two forces F1 and F2 act on a 5 kg mass. (a) If F1 = 20 N  and F2 = 15 N , find the acceleration of the
object. (b) If the two forces act in opposite directions, what would the acceleration be for the object?