2Acceleration Lab I: 𝑎 ∝ 1 𝑚 Acceleration is inversely proportional to How does the acceleration of a system depend on the mass of the system?Acceleration is inversely proportional tomass𝑎 ∝ 1 𝑚
3𝑎 ∝𝐹 Acceleration Lab II: How does the acceleration of a system depend on the force applied to the system?Acceleration is directly proportional the force applied𝑎 ∝𝐹
4Combining the results… 𝑎= 𝐹 𝑚This equation incorporates both of the previous relationships in one expression.- greater force larger acceleration- greater mass less acceleration
5Newton’s Second LawThe acceleration of an object is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.𝑎= 𝐹 𝑚
6A conceptual comparison of the 1st and 2nd laws of Newton… Newton’s First LawNewton’s Second Law
7Elevator Lab summary Upward acceleration occurs when… Moving upwards and speeding up (leaving a lower floor going up)Moving downwards and slowing down (stopping at a lower floor)*Scales read more than normal weightDownward acceleration occurs when…Moving downwards speeding up (leaving a higher floor going down)Moving upwards and slowing down (stopping at a higher floor)*Scales read less than normal weight
8Problem solving with unbalanced forces Draw a force diagram to represent the situationUse your force diagram as a guide for writing force equations…pay close attention to the directions of forces (F = ma)Remember that acceleration is also a vector quantity…it has direction too!
9ExampleA 25 kg bucket is lifted by a rope with an upwards acceleration of 1.5 m/s2. Find the tension in the rope.
10ExampleA 50 kg girl in an elevator accelerates downward at a rate of 3.0 m/s2. How much force does the floor exert on the girl?
11Example – forces at angles A 15 kg lawn mower is pushed with a force of 100.0N directed along the handle at 40° to the horizontal.If the frictional force on the mower is 30 N, determine the acceleration.Calculate the normal force on the mower
12FrictionFriction is a force that opposes the motion, or tendency of motion, of an object.Friction is caused mostly by the electromagnetic interactions of particles within molecules at the surfaces of objects in contact.
13Two Basic Types of Friction Static frictionexists between the surfaces of non-moving objects that are trying to moveMaximum static friction refers to the most force that can be applied before the object starts to moveKinetic friction (also called sliding friction)Exists between the surfaces of objects when there is relative motion between the objects
14Coefficient of Friction The coefficient of friction is the slope of a friction vs. normal force graph for two given surfacesIt is the ratio of the magnitudes of frictional force to the normal force acting between two surfaces.μ = f/FNSince this is a ratio of force to force, there are no units for the coefficient of frictionThis is an experimentally determined value for any two surface combinations.
15Coefficient of Friction The coefficient for static friction (μs) is generally larger than that of kinetic friction (μk) between surfaces.A common substitution to be made in problem solving will be f = μFN.If working with static friction, this equation represents a maximum possible value.
16Example – kinetic, constant speed The coefficient of friction between a 12 kg wooden crate and the floor is How much force is needed to push this crate across the floor at a constant speed?
17Example – accelerated motion A 5.0 kg box is pushed horizontally across the floor with a force of 25.0 N. If the coefficient of kinetic friction is 0.24, what is the acceleration of the box?