This is really frustrating me!!!?

Question

A spring gun (k = 25 N/m) is used to shoot a 56 g ball horizontally. Initially the spring is compressed by 16 cm. The ball loses contact with the spring and leaves the gun when the spring is still compressed by 12 cm. What is the speed of the ball when it hits the ground, 1.3 m below the spring gun?

Answer 1

PART1:
find the initial energy stored in the spring: kx^2=25*(0.16)^2
find the final energy stored in the spring: 25*(0.12)^2
subtract: 25*[(0.16)^2-(0.12)^2] = E

this is the total energy transferred to the ball.

find its horizontal speed : E=(m(v_x)^2)/2 -> v_x

PART2:
calculate the vertical speed required for the ball when it hits the ground:
v_y=gt (since it has no initial vertical velocity)

combine the two components of the velocity
v=squareroot(v_x^2 + v_y^2)

put in the values and there you go...

Answer 2

easy

for a spring, I hope you know that the force is the constant k, times the distance, d

and the work done is the force times the distance, in this case the integral, from 0.12 to 0.16, of the function k*d

which is (k/2)*d^2, from 0.12 to 0.16

which is (25/2)*(0.16^2-0.12^2) = 0.14 J (Joule)

this energy gets transferred to the ball, in the form of kinetic energy

the formula for kinetic energy is
Ec = (1/2)*m*v^2

so V = sqrt(2*Ec/m)

Ec is the 0.14 above
m is given as 0.056 (kilos)

so V = sqrt(2*2.5) = sqrt(5) = 2.236 m/s

that's, we are told, the horizontal component of the speed, Vx. Assuming there is no air resistance, this will stay constant.

however, as soon as it leaves the muzzle, the ball will also start falling, with acceleration g=9.81m/s^2 obviously

using some of the equations i'm sure you know, we have V=sqrt(2*a*x)

so here, V=sqrt(2*9.81*1.3)=5.05 m/s, when the ball hits the ground. this is the vertical component of the speed, Vy

now as for the MAGNITUDE of the velocity vector, this is sqrt(vx^2+vy^2)=5.523 m/s


this should help?

Answer 3

I can't answer your question because you didn't include the gravity (what planet?) nor the air resistance. Both would affect the answer.

Answer 4

Please indicate which speed you are talking about : horizontal, vertical, or composite ?