Lyzinski Physics CRHS-South Newton s Second Law Let s Review. Newton s 1 st Law says An object in motion (or at rest) tends to stay in motion (or at rest) unless acted upon by an unbalanced, external force. Included in this statement is the fact that objects naturally like to be either at rest or moving at a constant velocity. Their inertia keeps them in one of these two natural motion states, and it requires an unbalanced, external force to knock them out of their preferred motion state. Many forces can act on an object at rest, but unless the forces are unbalanced, the object will not move. The same can be said for objects moving at a constant velocity. Now for the one million dollar question. What happens to an object IF an unbalanced, external force DOES act upon it? The answer is simple: its motion will change. In other words, it will accelerate. Newton s 2 nd Law explains what will happen to this object. Stated in the simplest terms, it says Implied by this law are two proportions, namely F NET = ma In other words, if you double the net force acting on an object, the acceleration will double. If you quarter the net applied force, the acceleration will be quartered. Also, if you double the mass of an object, the applied force needed to accelerate it (at a certain rate) must also be doubled. If the mass of an object is tripled, the applied force must also be tripled in order to accelerate it at the same rate. Newton s 2 nd law has a vector nature. This is REALLY important. It can be broken down into both the x-direction and the y-direction as follows: and F x = ma x and F y = ma y This is pretty simple to understand. The net force in the x-direction will accelerate the object in the x-direction. Therefore, to find the acceleration in the x-direction, you divided the force (in the x- direction) by the mass. The same rule applies for the y-direction. Therefore, when using Newton s 2 nd Law, you always need to look at the direction that the object is accelerating, and only deal with the forces in that particular direction. If the object is not moving in a certain direction, can you still use Newton s 2 nd Law? Of course. However, you use F NET = ma = m(0) = 0, which says that the net force must be zero in the direction that the object is NOT moving in. When dealing with objects and the forces acting on them, it is important to look at ALL the forces. These forces include * Friction * Air resistance (a form of friction) * Pushes * Pulls (which included tensions coming soon) * Weight * Normal Forces (huh?)
Free-Body Diagrams Before using Newton s 2 nd Law (F=ma) it is often helpful to draw a free-body diagram, FBD of the object in question. This helps to visualize which forces are acting on the object so that you can use F=ma properly. The following list gives some common scenarios as well as the forces that are acting on the object in each case. Block resting on the ground Block falling through the air Pulling a box along the ground Pushing a block along the ground Block sliding down an inclined plane A key phrase: constant velocity When you see this phrase, realize that F NET = ma, and that a = 0, which means that F NET = 0.
In-class examples (part A) 1) An 50 kg object is accelerating at a rate of 5 m/s 2 to the right. Find the net force acting on the object. 2) Three forces (50N [S], 60N [W], and 30N [E] ) act simultaneously upon a 30 kg object. Find the object s acceleration. 3) A man pushes a 60 lb lawnmower across the grass with a constant horizontal force of 30N. If the lawnmower moves with a constant velocity, find the force of friction opposing the lawnmower s motion. 4) A box is accelerated from rest along a frictionless surface by a net force of 100N. It covers 40 meters in 5 seconds. Find the mass of the box. 5) A father (80 kg) pulls his son (30 kg) in a radio-flyer wagon (10 kg). The handle of the wagon makes an angle of 40 o with the horizontal, and the dad pulls with a force of 200N. First, draw an FBD (free-body-diagram) of this situation, showing all the forces acting on the wagon. Then, find the acceleration of the wagon if a) the ground is frictionless (which, by the way, is highly unlikely) b) the ground provides a constant frictional force of 30N. Homework Problems (part A) 1. A 5 kg box is sitting at rest on a perfectly frictionless surface. Suddenly, a 100 N forces pulls it eastward. Find the acceleration of the box. 2. A 300 kg block is sitting at rest on a perfectly frictionless surface. Two 25N forces act on the block, one directed east and one directed west. Find the acceleration of the block. 3. A block of unknown mass sits on a perfectly frictionless surface. It is pulled by a force of 100 N [S] and pushed by a force of 50 N [N]. The magnitude of its acceleration is 9 m/s 2. Find the mass of the block as well as the direction of the acceleration. 4. An object is pulled in two opposite directions along a frictionless surface by forces of 50 kn [E] and 30 kn [W]. If the object is accelerated at 5 m/s 2, find the object s mass. 5. A 40 kg box is pulled from rest at an angle of 30 o above the horizontal with a constant force of 500N. If the force of friction opposing the motion is 100N, find the box s acceleration parallel to the ground. Now use an equation of motion to figure out how far will it move in 7 seconds? What will its velocity be after these 7 seconds? 6. A 100 kg block is sitting on a perfectly frictionless surface. A force of 200 N directed at an angle of 30 o above the horizontal pulls the block. Find the acceleration of the block parallel to the ground. 7. A block is pulled along a surface at a constant velocity by a force of 200 N. Find the force of friction opposing the movement. 8. A 60 kg block is being pulled along a surface by a force of 100N. If the magnitude of the block s acceleration is 1.2 m/s 2, find the force of friction opposing the movement. Start off by drawing a full Free-Body-Diagram (FBD) of the block. 9. A 1.0 kg toy car is moving across a smooth floor with a velocity of 5.0 m/s. An unbalanced force of 2.0 N acts on the car for 4.0 s. Determine the velocity of the car at the end of the interval if the force acts in the opposite direction to the motion of the car.
The Force due to Gravity (Weight) Force due to gravity: A field force (a vector quantity) that always is directed towards the center of the earth. Weight: The magnitude of the Force due to gravity. g earth = 9.8 m/s 2 g moon = 1.6 m/s 2 Mass: A measure of an objects inertia (its tendency to resist a change in its motion). Inherent property of an object. Weight: Decreases as you move away from the center of the earth. NOT an inherent property of an object Examples: a) Find the earth weight of an object whose mass is 60 kg. b) If an object weighs 700N on the moon, what is its mass on the moon? What is its mass on the earth? Side Views vs. Views from Above Pushing a box along the ground ground
In-class examples (part B) 1) A 30 kg box is pushed along a surface. The person pushing the box pushes with a constant force of 300 Newtons directed at an angle of 30 o below the horizontal. If the box starts from rest and reaches a speed of 5 m/s after only 2 seconds of pushing, find the force of friction acting on the box. Make sure to start with a complete FBD of the box, showing all the forces acting upon it. 2) A skydiver of mass 75 kg is falling through the non-physics-land air. Eventually he reaches a terminal velocity and falls at a constant speed. Find the resistive force (from the air) that acts on the skydiver at this time. Make sure to start with a complete FBD, showing all the forces acting upon the skydiver. 3) Explain the relationship between Newton s 1 st Law and his 2 nd Law. Homework Problems (part B) 10. An electron has a mass of 9.1 x 10 31 kg. Between the electrodes of a cathode-ray tube, it moves a distance of 4.0 mm, accelerated by a net electrical force of 5.6 x 10 15 N. Assuming that it started from rest, find its acceleration and its final velocity. 11. A bullet of mass 20 g strikes a fixed block of wood at a speed of 320 m/s. The bullet embeds itself in the block of wood, penetrating to a dept of 6.0 cm. Calculate the average net force acting on the bullet while it is being brought to rest. 12. A 2 kg block is pulled across a frictionless surface by forces of 5N [E], 16 N [SW], and 10 N [S 30 E]. Find the magnitude and direction of the block s acceleration. 13. A 9 kg ball falls through the air, which resists the ball with a constant force of 9N. Draw a freebody diagram of the ball and then find its acceleration. Why is the acceleration of the ball NOT equal to g? Fully explain. 14. If an object is moving at a constant velocity, explain what Newton s 2 nd law says about the object. Does this agree with or disagree with Newton s 1 st Law. 15. A 3-car train is being pulled on frictionless tracks. The lead car is has a mass of 2000 kg, while the 2 nd two cars each have masses of 1500 kg. How much force is required to accelerate the train at 3 m/s 2? If the train is being pulled by this force and the last car suddenly detaches, what will its new acceleration be? 16. Two girls pull a sled from rest across a field of snow, as shown in the diagram. A third girl pulls backward with a 2.0 N force. All forces are constant. If the mass of the sled is 10 kg, determine its instantaneous acceleration. Then, determine the time required for the sled to move a distance of 10 m. (A view from above, or a bird s eye view, is assumed in this problem) 2 N 10 kg 10 N 30 40 10 N