In a perfectly elastic collision, both momentum and kinetic energy are conserved. Consider a perfectly elastic collision in one dimension between two objects in which the second object is initially at rest. The final velocities of each object are given by: (v1)f =)m1 − m2/m1 + m2)*(v1)i (v2)f =(2m1/m1 + m2)*(v1)i Derive these formulas, starting from the corresponding conservation equations: momentum: m1(v1)i = m1(v1)f + m2(v2)f kinetic energy: 1/2m1(v1)^2i=1/2m1(v1)^2f +1/2m2(v2)^2f

As shown in the figure (Figure 1), a superball with mass m equal to 50 grams is dropped from a height of hi=1.5m . It collides with a table, then bounces up to a height of   hf=1.0m . The duration of the collision (the time during which the superball is in contact with the table) is tc=15ms . In this problem, take the positive y direction to be upward, and use g=9.8m/s2 for the magnitude of the acceleration due to gravity. Neglect air resistance. Find Jy, the y component of the impulse imparted to the ball during the collision. Express your answer numerically, to two significant figures.   Find the y component of the time-averaged force Favg,y, in newtons, that the table exerts on the ball.   Find Kafter−Kbefore, the change in the kinetic energy of the ball during the collision, in joules.

You have two vectors: A = 7.271 +3ĵ and B = 4î - 0.95ĵ+ 12k. If vector A represents an initial momentum vector, and vector B represents a final momentum vector, what is the y component of the impulse? If you think your answer is negative, do include the negative sign with your result.

Two rolling carts are moving toward each other at the same speed. Cart 1 has a mass m1 =200g and Cart 2 has a mass m2 =400g. Draw a velocity vector v → for each cart. Momentum p → is a vector defined as p → = m v →. Draw a momentum vector for each cart. Then add the two momentum vectors together to find the total momentum, vector P total =vector p1 + vector p2

Suppose a toy truck with a mass of m = 1 kg is moving with a speed of v = 1 m/s. What is the magnitude (in kg • m/s) of its momentum, p?

For all the collisions in this lab, what can you conclude about the sum of the changes in momentum for the objects (Δp1 + Δp2 for Parts 1 and 2 and  Δp1 + Δp2 + Δp3 for Part 3)? Does this agree with the Law of Momentum Conservation? Show why or why not.

Why is the selected answer wrong? What is the correct answer?

For an isolated system where two masses collide in two dimensions (2D), check all TRUE statements: Piy = Pfy J = 0, since the x and y components cancel each other out. If the masses collide in 2D, the collision must be inelastic. Pfx =Pix If the collision is inelastic, the final momentum, Pf, can be derived by the vector addition of the momentum vectors of the two masses prior to collision.

this is a multi step problem but I am just having trouble with this part of the problem. Here are the values that I correctly calculated: mass of particle 1=6 kg initial velocity for particle 1= 185i+138j final velocity for particle 1= -68.89i+-50.67j F21=-15.9e-t/96i+-100sin(2πt/96)j I am trying to find: What is the x displacement for particle 1? I think that I need to use Newtons second law to get an expression for acceleration, and then integrate but I am not getting the right answers.

Suppose two particles are traveling along the space curves r1(t)=< t2,, 8t-16, t2 > and r1(t)=< 3t+4, t2, 5t-4, >.  A collision will occur when the two particles arrive at the same point at the same time.  Find any time(s) and location(s) when and where the particles collide