block and spring problem?

Question

A 15.0 kg block is attached to a very light horizontal spring of force constant 550 N/m and is resting on a smooth horizontal table. Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.

Answer 1

You can conserve energy and momentum here. Start with momentum.

p1 = ms*vs1 = p2 = ms*vs2 +mb*vb

vs1 = 8 m/s, ms = 3 kg, vs2 = -2 m/s, mb = 15 kg

Solve for vb ---> vb = ms*(vs1 -vs2)/mb = 3*(8- (-2))/15 = 2 m/s

Now use conservation of energy

K = 1/2mb*vb^2 = 1/2k*x^2 and solve for x

x =vb*sqrt(m/k) = 2*(sqrt(15/550)) = 0.33 m

Answer 2

2 smart issues to contemplate in incredibly much any mechanics undertaking are forces and skill. checklist each and every of the forces interior the equipment with direction and as much as you comprehend approximately their magnitude. perceive the skill skill and kinetic skill at key factors in time, and be sure the place any transformations in skill have long gone. jointly as the block is in action, there are 4 forces on it: Gravity and the traditional rigidity stability one yet another (there is not any internet vertical rigidity). The spring pushes or pulls in direction of its equilibrium factor. Its magnitude is kx. Friction pushes interior the direction opposite the block's action. Its magnitude is ?mg. the skill skill of the compressed spring is a million/2 ok (x1)^2. Its kinetic skill is 0. the skill skill of the completely stretched spring is a million/2 ok (x2)^2. Its kinetic skill is likewise 0. The replace in skill of the block might desire to equivalent the artwork finished by utilising friction. The equation is: ?KE = F * d a million/2 ok (x2)^2 - a million/2 ok (x1)^2 = -?mg * (x2 - x1) notice that i've got made friction unfavourable, because of the fact i'm determining on enhance of the spring to be the advantageous direction (x1 = -5.0 cm and x2 = 2.3 cm).