Figure 9.8,9 Impulse

• Two balls of equal mass (m=0.15 kg) … Eventually the two balls collide, and after the collision the red ball is moving at 5.0 m/s and the blue ball is moving at 3.0 m/s.What was the change in momentum of the blue ball? What was the change in momentum of the red ball? Was momentum conserved in this collision? (most got this 14 right, 5 ok but signs reversed; 9 had various problems with units etc. 18 no answer)

• The change in momentum for the blue and the red ball are both 2.0 m/s. The momentum is conserved. For collisions of bodies of equal mass, the 2 balls simply exchange velocities.

• p=mv. p(red)=3x.15kg=.45 p(blue)=5x.15=.75• For the blue ball: p'=m(v2-v1) = 0.15kg*(3.0 m/s -

5.0 m/s) = -0.3kgm/s For the red ball: p''=m(v2-v1) = 0.15kg*(5.0 m/s - 3.0 m/s) = 0.3kgm/s

3.0 m/s5.0 m/s

• Under what circumstances (if any) will linear momentum NOT be conserved in a physical process? (19 correct, 8 off slightly; 18 no answer)

• if the collision is inelastic, linear momentum is mot conserved in the process. (Energy is not the issue here!)

• there are no circumstances when linear momentum would not be conserved.

• Linear momentum will not be conserved if a net external force acts on the system of momentum will not be conserved.

• Momentum will be conserved to the extent that external forces are negligible compared to the forces between the interacting objects!

Figure 9.8,9 Impulse

Chapter 9 problems

b. What was the direction of travel before the explosion?

Chapter 9 problems

Chapter 9 problems

• A red ball moves on a frictionless horizontal plane along the black line and collides with a stationary blue ball, the two balls then proceed along the red and blue lines respectively. At some time later, the two balls are at the positions marked by the circles with the black borders. Which ball has the greater mass?

• (Equal:1 Red: 21 Blue 4 No answer: 19)

• The blue ball has a greater mass because both appear to be the same distance from the point of collision and the red ball had a greater velocity. (several responses focused on distance the two balls traveled).

• The blue ball has a greater mass because v2f = (2m1/m2)v1i, and the quantity in the parenthesis indicates that the

• The red ball must have more mass than the blue ball. If the masses were equivalent, the red ball would not move after the collision. However, the red ball does move, thus it must have a greater mass. (BE CAREFUL, this is only true for 1-D collisions, this collision is in 2-D!!)

• I think the blue ball has greater mass because the red ball is deflected off its original trajectory. (This is the key, and about 6 or 7 focused on this aspect).

• The key is to focus on the momentum perpendicular to the incident momentum!

• Clearly (I think) the y component of the blue ball’s velocity is greater than the red’s. Since the y component of the total momentum must be zero after the collision, the red ball MUST be more massive.

yx

Now let’s analyse thisProblem more completelyVby = 5 Vry

pbx = pry

Vrx ~ 6 Vry

(Can’t really compare initial and final speeds directly from the figure since time information not given).

Basic ideas (for sheet)• Work = F.d W = K Power = dW/dt (=F.v)• Kinetic Energy: K = ½ mv2

• P.E.: Ug = mgh Uel = ½ k(x-xo)2

• F = -dU/dx (e.g. Spring: F = -k(x-xo))• Mech. Eng. conserved if only conservative forces do work.

Dissipative forces convert some Mech. Eng. to thermal energy.

• Center of Mass R = (miri)/mi

• Impulse: J=P = Fav t = integral of F(t)dt• P= mv Fnet = dP/dt => momentum is conserved if

outside forces can be neglected compared to internal forces.

• Defns: Elastic, Perfectly inelastic, etc. for collisions, Conservative forces, dissipative forces etc. BEWARE of applying 1-D ideas to multiple dimensions (or elastic equations to partially inelastic problems etc.).

Calm inquiries

• Collisions (5 people)

• Setting up problems (4 people)

• Work/Power (3)

• Energy Conservation (2)

• Momentum conservation (2)

• Potential Energy Curves (1)

Chapter 9 problems

Chapter 7 problems

Chapter 8 problems

e). What is the force on the particle at the left turning point?