Unbalanced Forces

Acceleration 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 to mass 𝑎 ∝ 1 𝑚

𝑎 ∝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 applied 𝑎 ∝𝐹

Combining the results… 𝑎= 𝐹 𝑚 This equation incorporates both of the previous relationships in one expression. - greater force  larger acceleration - greater mass  less acceleration

Newton’s Second Law The 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

A conceptual comparison of the 1st and 2nd laws of Newton… Newton’s First Law Newton’s Second Law

Elevator 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 weight Downward 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

Problem solving with unbalanced forces Draw a force diagram to represent the situation Use 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!

Example A 25 kg bucket is lifted by a rope with an upwards acceleration of 1.5 m/s2. Find the tension in the rope.

Example A 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?

Example – 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

Friction Friction 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.

Two Basic Types of Friction Static friction exists between the surfaces of non-moving objects that are trying to move Maximum static friction refers to the most force that can be applied before the object starts to move Kinetic friction (also called sliding friction) Exists between the surfaces of objects when there is relative motion between the objects

Coefficient of Friction The coefficient of friction is the slope of a friction vs. normal force graph for two given surfaces It is the ratio of the magnitudes of frictional force to the normal force acting between two surfaces. μ = f/FN Since this is a ratio of force to force, there are no units for the coefficient of friction This is an experimentally determined value for any two surface combinations.

Coefficient 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.

Example – kinetic, constant speed The coefficient of friction between a 12 kg wooden crate and the floor is 0.32. How much force is needed to push this crate across the floor at a constant speed?

Example – 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?