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in Physics by (70.7k points)

As shown, a 0.20-kilogram mass is sliding on a horizontal, friction less air track with a speed of 3.0 meters per second when it instantaneously hits and sticks to a 1.3-kilogram mass initially at rest on the track. The 1.3-kilogram mass is connected to one end of a mass less spring, which has a spring constant of 100 newtons per meter. The other end of the spring is fixed.

a. Determine the following for the 0.20-kilogram mass immediately before 

i. Its linear momentum 

ii. Its kinetic energy the impact. 

b. Determine the following for the combined masses immediately after 

i. The linear momentum 

ii. The kinetic energy

After the collision, the two masses undergo simple harmonic motion about their position at impact. 

c. Determine the amplitude of the harmonic motion. 

d. Determine the period of the harmonic motion.

1 Answer

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Best answer

(a) (i) p = mv = (0.2)(3) = 0.6kg m/s 

(ii) K = ½mv2 = ½ (0.2)(3)2 = 0.9J 

(b) (i) Apply momentum conservation pbefore = pafter = 0.6 kgm/s 

(ii) First find the velocity after, using the momentum above 

0.6 = (1.3 + 0.2)vf 

vf = 0.4m/s, then find K, K = ½ (m+ m2) vf2 = ½(1.3+0.2)(0.4)2 = 0.12J 

(c) Apply energy conservation 

K = Usp 

0.12J = ½ k∆x2 = ½ (100)∆x2 

∆x = 0.05m

(d) Period is given by

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