A 1.6 kg cart moving at 6.0 m/s [E] collides with a 1.2 kg cart moving at 3.0 m/s [W]. The head-on collision is completely elastic and is cushioned by a spring. A student was asked to find the spring constant given that the maximum compression of the spring during the collision is 1.2 cm. a) Explain each step in their solution. (1.6) (6) (1.2)(-3) = (2.8)(v1) 1 V₁ = 2.14 m/s 1 2 (1.6) (6²) + ½ (1.2)(-3)² = (2.8) (2.14)+k( 2 k = 385714.29 Statement: The spring constant is 390 000 N/m b) What would the spring constant be if the maximum compression was 2.4 cm instead? Why?

A skater of mass 40 kg is carrying a box of mass 5 kg. The skater has a speed of 5 m/s with respect to the floor and is gliding without any friction on a smooth surface. a. Find the momentum of the box with respect to the floor. b. Find the momentum of the box with respect to the floor after she puts the box down on the frictionless skating surface.

Check Your Understanding Notice that the mass of the air in the tank was neglected in the analysis and solution. How would the solution method changed if the air was included? How large difference do you think if would make in the final answer?

A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 3.0 m/s, what is the maximum mass of grain that it can accept?

A ball of mass 250 g is thrown with an initial velocity of 25 m/s at an angle of 30 with the horizontal direction. Ignore air resistance. What is the momentum of the ball after 0.2 s? (Do this problem by finding the components of the momentum first, and then constructing the magnitude and direction of the momentum vector from the components.)

For the preceding problem, find the final speed of the case of each sled for the case of an elastic collision.

A head-on, elastic collision occurs between two billiard balls of equal mass. If a red ball is traveling to the right with speed v and a blue ball is traveling to the left with speed 3v before the collision, what statement is true concerning their velocities subsequent to the collision? Neglect any effects of spin. (a) The red ball travels to the left with speed v, while the blue ball travels to the right with speed 3v. (b) The red ball travels to the left with speed v, while the blue ball continues to move to the left with a speed 2v. (c) The red ball travels to the left with speed 3v, while the blue ball travels to the right with speed v. (d) Their final velocities cannot be determined because momentum is not conserved in the collision. (e) The velocities cannot be determined without knowing the mass of each ball.

A 5.0-g egg falls from a 90-cm-high counter onto the floor and breaks. What impulse is exerted by the floor on the egg?

I need help with the following physics problem. Thanks

Consider a one-dimensional elastic collision in which a moving ball A collides with a stationary ball B.  Assume that the two balls have equal masses. a) Write an equation for the conservation of momentum of the system. (Make use of p=mv.) b) Write an equation for the conservation of kinetic energy of the system. (Make use of KE = 1/2mv2 c) Solve the two previous equations simultaneously and discuss the implications of this result on the possible final velocities of the first and second balls.