Help with elastic collisions/kinetic energy problems

[PhilliesFan]

(1)Block A of mass mA = 1kg is moving at velocity +v (from left to right)
towards block B of mass mB = 2kg which is at rest. To the right of block B there is block
C. It is at rest and its mass is mC = 1kg. Find the ultimate velocities of all three masses
assuming all collisions are elastic (i.e. total kinetic energy does not change).

(2) A 0.05 kg marble is fired vertically upward using a spring gun. The spring
must be compressed 8 cm if the marble is to just reach a target 20 m above the marble’s
position on the compressed spring. (a) What is the change ∆Ugrav in the gravitational
potential energy of the marble-Earth system during 20 m ascent? (b) What is the change
∆Uelas in the elastic potential energy of the spring during its lunch of the marble? (c)
What the elastic (spring) constant of the spring?

(3) A person of mass M = 32.5 kg stands on ice and disdainfully throws my
favorite Leo Tolstoy’s book ”Anna Karenina” weighing m = 2.25kg with the initial velocity
v0 = 12m/s. The book is thrown from the ice level, so the initial height is zero. When the
book lands on the ice the total distance between the book and the offender is l = 15.2 m.
At what angle was this excellent book thrown? How fast is the offender moving?

 

[RobLikesBrunc]

Show us your attempt for each problem and where you're having trouble.

 

[SammyS]

(1)Block A of mass mA = 1kg is moving at velocity +v (from left to right)
towards block B of mass mB = 2kg which is at rest. To the right of block B there is block
C. It is at rest and its mass is mC = 1kg. Find the ultimate velocities of all three masses
assuming all collisions are elastic (i.e. total kinetic energy does not change).

(2) A 0.05 kg marble is fired vertically upward using a spring gun. The spring
must be compressed 8 cm if the marble is to just reach a target 20 m above the marble’s
position on the compressed spring. (a) What is the change ∆Ugrav in the gravitational
potential energy of the marble-Earth system during 20 m ascent? (b) What is the change
∆Uelas in the elastic potential energy of the spring during its lunch of the marble? (c)
What the elastic (spring) constant of the spring?

(3) A person of mass M = 32.5 kg stands on ice and disdainfully throws my
favorite Leo Tolstoy’s book ”Anna Karenina” weighing m = 2.25kg with the initial velocity
v0 = 12m/s. The book is thrown from the ice level, so the initial height is zero. When the
book lands on the ice the total distance between the book and the offender is l = 15.2 m.
At what angle was this excellent book thrown? How fast is the offender moving?

Hello PhilliesFan. Welcome to PF !

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Thanks.

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