1.7.1 The Concept of Force Defined as: any influence which tends to change the motion of an object. 1.7.1a The Fundamental Forces The four fundamental forces, arranged in increasing order of strength, are: 1. The Force due to Gravity The weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large scale structure of galaxies, stars, etc. It is an example of an inverse square law force. The force is always attractive and acts along the line joining the centers of mass of the two masses. The forces on the two masses are equal in size but opposite in direction, obeying Newton's third law. Viewed as an exchange force, the massless exchange particle is called the graviton. 2. The Weak Nuclear Force 18 An extremely short range exchange force (10 m. approx. the size of a proton) that involves the exchange of the W and Z intermediate vector bosons. It is involved in many decays of nuclear particles and is essential to the formation of deuterium which is used by the sun during fusion. Its most familiar effect is beta decay (of neutrons in atomic nuclei) and the associated radioactivity. The word "weak" derives from the fact 13 that the field strength is some 10 times less than that of the strong force. 3. The Electromagnetic Force This force holds atoms and molecules together. It manifests itself through the forces between charges (Coulomb's Law) and the magnetic force, both of which are summarized in the Lorentz force law ( ). The electromagnetic force is an exchange force involving the exchange of photons. It has infinite range and it obeys the inverse square law, like the force due to gravity. 4. The Strong Nuclear Force This force holds the nucleus together against the enormous forces of repulsion of the protons. However, it is not an inverse square force like the electromagnetic force and it has a very short range. It has been modelled as an exchange force in which the exchange particles are pions and other heavier particles. Page 1 of 12
1.7.1b The Units of Force 2 The SI unit for force is the Newton, which is defined by 1 Newton = 1 kg m/s as you may recall from Newton's second law. 1.7.1c Common Forces In our everyday lives, we usually experience forces like the ones listed below: the force due to gravity (directed downward) tension (along the rope) friction (opposes the motion) normal (perpendicular to the surface) Eg.#1 Label these forces on the diagram above. 1.7.2 Drawing Free Body Diagrams When analyzing situations involving forces, it is much easier to determine the net effect of all of the forces if we draw a simpler diagram called a free body diagram. A free-body diagram is a simplified sketch of a situation where: i) the object is replaced by a point ii) all the surrounding objects are stripped away iii) all of the forces acting on the body are indicated by force vectors drawn to scale that originate at the point drawn in (i) above Eg.#2 Draw a free-body diagram of a bicyclist that is traveling on a road inclined at 30 degrees that experiences the following forces: the force due to gravity: 780 N [down] the normal force: 680 N [perpendicular to the plane of the road surface] the friction force: 390 N [up the incline] Elevation view Free-body diagram Page 2 of 12
Eg.#3 Draw an FBD for each of the following: a) A hot dog sits on a table. b) A length of railway track is being raised at a constant speed by a cable connected to a crane. c) A pencil has just begun falling d) A stove is being pulled up a ramp into from a desk to the floor (assume that a delivery truck by a cable parallel to the air resistance is negligible). ramp. The ramp is at an angle of 18 above the horizontal. Eg.#4 Draw an FBD of a ball that is dropped from a tall building assuming there is a force of friction caused by air resistance. a) shortly after it leaves b) two seconds later c) when it reaches terminal speed your hand, Page 3 of 12
Eg.#5 The tourist at right is pulling a heavy suitcase at a constant velocity to the right with a force applied to the handle at an angle above the horizontal. A small force of friction resists the motion. a) Draw an FBD of the suitcase, labeling b) Draw an FBD of the suitcase, labeling the components of the appropriate forces. the components of the appropriate Choose the direction of motion to be the forces. Choose the +x direction as the +x direction. direction in which the handle is pointing. c) Which choice of +x is more convenient? Explain your answer Choosing the direction in which the handle is pointing means that only one force needs to be resolved into two components, making the analysis easier. d) How do you know which reference frame to choose? Explain your answer. Choose the reference frame that includes the acceleration. This will make Newton s second law much easier to apply as the net force will not have to be broken into components. Page 4 of 12
1.7.3 Finding the Net Force 1.7.3a Finding the Net Force Using the Sine and Cosine Law Eg.#6 While competing, a long jumper whose weight is 538 N. experiences a force of 6380 N [68.3 back from the vertical] at the instant she lands. a) Draw a free body diagram to scale b) Find the net force on the jumper. Page 5 of 12
1.7.3b Finding the Net Force Using Vector Components Eg.#7 A boat pulling two water skiers is shown below: If the water applies a force of 450 N.[forward] on the boat and the water skiers each apply a force of 225 N. back on the boat in the directions shown above, a) draw a free body diagram of the boat to scale b) find the net force on the boat. Because of the symmetry of the situation, Page 6 of 12
Worksheet 1.7 1. You push your ruler westward across the desk at a constant speed by applying a force at an angle of 25 degrees above the horizontal. a) Name all of the forces acting on the ruler b) Draw a freebody diagram of the ruler Normal, friction, applied force and weight 2. Draw a freebody diagram for each of the following objects: a) A cup hanging from a hook b) A curling rock sliding freely in a straight line on a rink c) A person standing in an elevator that d) A crate being dragged across the is accelerating downward floor, with a significant amount of friction, by a person pulling on a rope at an angle of 23 degrees above the horizontal Page 7 of 12
3. The force of gravity on a textbook is 18N.[down] a) What is the net force on the book if b) Neglecting air resistance, what is the it is held stationary in your hand? net force acting on the book if you suddenly remove your hand? 4. At one particular instant in its flight, a ball experiences a force due to gravity of and an air resistance of. Calculate the net force on the ball. Page 8 of 12
5. Given the following force vectors: a) Draw a free body diagram to scale. b) Find the net force using the method of components. Page 9 of 12
c) Draw to scale. d) Find using the sine and cosine laws. Page 10 of 12
6. Given and determine the third force that must be added to the sum to produce a net force of zero. The required force is: Page 11 of 12
7. A crate is being dragged across the horizontal icy sidewalk by two people pulling horizontally on cords as shown below. The net horizontal force is. The tension in cord 1 is 27N[E]. If friction is negligible, determine the tension in cord 2. Page 12 of 12