A ball of mass m 1.85 kg les spring and compresses It a distance d- 7.90 cm as i

Question

A ball of mass m 1.85 kg les spring and compresses It a distance d- 7.90 cm as in Figure [b] shown below. Neglecting any energy losses during the collision, find the following. (a) Find the speed of the ball just as it touches the spring. This may be due to roundoff error, or you could have a mistalce in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. mys (b) Find the force constant of the spring kN/m Need Help? Meseln by exerting a

Explanation / Answer

a)

h = height = 53 cm = 0.53 m

using conservation of energy

Kinetic energy of the ball just before touching the spring = initial Potential energy of ball above the spring

(0.5) m v2 = mgh

v = sqrt(2 gh) = sqrt(2 x 9.8 x 0.53) = 3.22 m/s

b)

using conservation of energy between initial and final position of ball after the spring is compressed.

initial potential energy above the lowest point when the spring is compressed = spring energy

mg (h + d) = (0.5) k d2

(1.85) (9.8) (0.53 + 0.079) = (0.5) k (0.079)2

k = 3538.3 N/m

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