Class Notes 11 November Turn in / Pick up Homework Today: #3: Why ? This is not a surface! #4: Force of gravity doesn’t change b) Bottom because PE is greatest #5: Use variables; Draw a sketch Start with EA + WNC = EB. Today: Chapter 7: Impulse and Momentum

Linear Momentum We will define linear momentum as the mass times the velocity: p = mv

Power and momentum are, respectively, ___ quantities. Vector / Vector Scalar / Vector Vector / Scalar Scalar / Scalar Answer b is correct. 2016: 0, 9, 1, 3

Linear Momentum We will define linear momentum as the mass times the velocity: p = mv A vector quantity! Units: [p] = kg·m/s Connection to force… After this, bounce a ball off the table top. Discuss the short-lived forces involved.

Connection to Newton F = ma = m(Dv/Dt) =(Dmv/Dt) = Dp/Dt So Newton’s second law can be rewritten using momentum. A net force causes a change in momentum! Ex.-Impulsive Forces Impulse = FDt = Dp

…but F is not constant! F F Dt Blue box and labels appear on click. t

 F F F t t Dt Impulse = FDt = Dp Impulse = FDt = Dp Claim that the “area under the curve may be approximated as indicated.” t t Dt

Example: USC-Clemson A 400. g football resting on the ground is kicked so that it travels the maximum distance. It lands 70.0 m away, and the contact time was 48.0 ms. Estimate the force applied. What impulse is delivered? Max distance implies range, thus = 45°. F = 218N, Dp = 10.5 kg·m/s @45.0º

Forces and Momentum Consider one object: F = Dp /Dt First bullet is a statement of Newton’s First Law. For two objects… …Break up these forces onto the two individual particles. Consider both external and internal forces. Argue that the internal forces in the *system* drop out because of Newton’s Third Law.

If the net external force on an object is zero then… The momentum must be zero The momentum may be zero The momentum must not be zero It must accelerate Answer b is correct. 2016: 6, 6, 0, 0

Forces and Momentum SF1=Dp1/Dt SF2=Dp2/Dt Consider one object: if F = 0 then p = constant! Consider two objects: For any system of particles there may be a net force acting on the system… SF1=Dp1/Dt SF2=Dp2/Dt

So when the net external force acting on a system is zero the total momentum of the system does not change, which means, the total momentum (of the system) is conserved! pi = pf Mention how this concept is especially useful when analyzing collisions and explosions.

So when the net external force acting on a system is zero the total momentum of the system does not change, which means, the total momentum (of the system) is conserved! pi + Jext = pf Mention how this concept is especially useful when analyzing collisions and explosions.

Homework Read Chapter 7, sections 3-4 Do problems on Worksheet #30 Use impulse and momentum ideas to solve Warning: Velocity is a vector!