Newton’s 2 nd law problems ΣF = ma Or F net = ma

F = ma Determine the acceleration which result when a 12-N net force is applied to a 3-kg object and then to a 6-kg object. A)b)F = 12 N m = 3 kgm = 6 kg 12 = 3a12 = 6a A = 4 m/s 2 a = 2 m/s 2

A man is pulling a cart (total 8.7 kg) with a force of 168 N. Neglecting friction, how much time does it take to get the cart from rest up to 8 m/s? m = 8.7 kg F = 168 N Vo = 0 m/s V = 8 m/s t= ? Need to find acceleration first, F = ma 168 = 8.7aA = 19.3 m/s2 then solve acceleration for time a = (v-vo)/ t t = (v-vo) /a (8-0)/19.3 = 0.41 sec

ΣF = all the forces that are acting on that one object in the same plane added together. More than one force can act on an object at once. For example, two people could push on a book at the same time. One person could push toward the left and the other could push toward the right. In this case the two forces would act against each other. –If the force toward the left was greater than the force toward the right, then the prevailing force would be toward the left. The strength of this prevailing force would be the difference between the strengths of the two separate forces. In this prevailing force is called the net force. Basically, the word net means total.

For example, if one person pushed the book with a force of 20 Newtons toward the left, and the other person pushed the book with a force of 18 Newtons toward the right, then that the net force would be 2 Newtons in size and directed toward the left. –As you can see, the net force is aimed toward the left. This object will move as if it had a single force of 2 Newtons pushing on it toward the left.

Forces which are aimed to the right are usually called positive forces. And forces which are aimed to the left are usually said to be in a negative direction. –So, to be more accurate, in the above diagram we should call F1 a negative force, that is, negative 20 Newtons, and we should call F2 a positive force, or positive 18 Newtons. Since the net force is aimed to the left; it is a negative force. Thus, F net = -2N

If an object is not moving, are there any forces acting on it? Yes –No movement means the sum of the Forces = 0 N. –Example: an object resting on the table. The forces acting are: –The object pushing down on the table –The table pushing up on the object. –Neither of these forces act to cause any motion

What does it mean for an object to be moving at a constant speed? This means that there is no acceleration. This means that the sum of the forces acting on that object add up to zero.

Weight = mg T or F t = tension ΣF = T - mg = ma if something is pulling up and the weight is pulling down. Don’t forget other motion formulas such as V 2 = v o 2 + 2ad y = y o + v o t + ½ at 2 Decide which way is the motion and therefore the +y, and the acceleration.