Posted by **rachel** on Friday, November 7, 2008 at 11:58pm.

A child's game consists of a block that

attaches to a table with a suction cup, a

spring connected to that block, a ball, and a

launching ramp. By compressing the

spring, the child can launch the ball up the

ramp. The spring has a spring constant k,

the ball has a mass m, and the ramp raises a

height h. The spring is compressed a

distance S in order to launch the ball. When

the ball leaves the launching ramp its

velocity makes an angle Î¸ with respect to the horizontal.

(a) Calculate the velocity of the ball when it just leaves the launching ramp (both magnitude and

direction. Be sure to specify your coordinate system.)

(b) The spring constant = 1000.0 N/m, the spring's compression is 4.00 cm, the ball's mass is

55.0 grams, the height of the ramp is 15.0 cm, and the top of the table is 1.20 m above the floor.

With what total speed will the ball hit the floor? (Use g = 10.0 m/s2)

- Physics -
**bobpursley**, Saturday, November 8, 2008 at 3:50am
I assume you have to ignore friction, and assume the ball does not start to roll going up the ramp. Doing that, use energy considerations.

SpringcompressedEnergy + initialPE

=KE final

The initial PE is mg*1.35

solve for the total KE when it hits the floor, and from that, its speed.

I will be happy to check your work.

- Physics -
**rachel**, Saturday, November 8, 2008 at 4:09am
how come for part a. when i solve for Vf (which becomes V0 of the projectile motion), i get a negative value.. since i got this equation...

1/2ks^2+mgh+1/2mv^2 = 0

solving for v.. i get

v = sqrt(-(2gh-ks^2/m)

thats what is confusing me. so im not shure if i did it correctly.

- Physics -
**bobpursley**, Saturday, November 8, 2008 at 5:05am
SpringcompressedEnergy + initialPE

=KE final

1/2 k s^2+mgh=1/2 m v^2 This v is the velocity at the floor when it hits. h is the intial height of the ball (table). h is 1.20, not 1.35 as I indicated.

v=sqrt(2gh+ks^2/m)

The above is just sayingthe intial energy has to equal the final energy, and initial energy is spring energy + initial potential energy (mg*1.2)

- Physics -
**Michigan**, Sunday, February 13, 2011 at 10:33pm
this doesnt work

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