A ball, mass 0.77 kg, is placed in a spring-loaded cannon. The cannon is set hor

Question

A ball, mass 0.77 kg, is placed in a spring-loaded cannon. The cannon is set horizontally on a table, height of 1.50 meters off the floor. The spring is released, causing the ball to shoot off the table. The speed of the ball as it leaves the cannon is 5.30 m/s. Thus you know the Kinetic Energy as it leaves the cannon. Calculate the kinetic energy of the ball as it leaves the cannon. Calculate the kinetic energy of the ball just before it hits the floor. Calculate the final speed, voag just before hitting the floor. Calculate the energy stored in the spring. If the spring constant is 60 N/m, how far did you compress the spring? (Extra credit) The actual speed of the ball just before hitting the floor is measured. It turns out that the MEASURED speed was slightly less than the value you calculated in part (c) above, 0.95vfinai- This loss is due to air drag acting on the ball. So, taking the measured speed as 0.95 of the value you obtained in (c), find the energy lost due to air drag.

Explanation / Answer

a) KEi = 0.5*m*v^2

= 0.5*0.77*5.3^2

= 10.81 J <<<<<<<<------Answer

b) KEf = KEi + m*g*h

= 10.81 + 0.77*9.8*1.5

= 22.13 J <<<<<<<<------Answer

c) KEf = 0.5*m*vf^2

==> vf = sqrt(2*KEf/m)

= sqrt(2*22.13/0.77)

= 7.58 m/s <<<<<<<<------Answer

d) Energy stored in the spring, U = KEi = 10.81 J

e) U = 0.5*k*x^2

==> x = sqrt(2*U/k)

= sqrt(2*10.81/60)

= 0.6 m <<<<<<<<------Answer

f) The enrgy lost due to air drag = KEf*0.05^2

= 22.13*0.05^2

= 0.055 J <<<<<<<<------Answer

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