Question

A worker pushing a 2 kg dolly loaded with a 233 kg statue receives a text. While checking his phone, he loses control of the cart, which is rolling at 1.00 m/s. This statue collides with another statue, 169 kg, that has just exited the kiln and reached a 0.229 m/s maximum velocity. a. If the collision is perfectly bouncy, what are the final velocities of the two statues?

b. The just-cooked statue actually fractures a little bit due to the impact. If the collision actually loses 20% of the total energy to damage to the statue, what will the final velocities be instead?

Answer 1

a)

m = mass of dolly = 2 + 233 = 235 kg

v1i = initial velocity of dolly = 1 m/s

M = mass of statue = 233 kg

v2i = initial velocity of statue = 0.229 m/s

v1f = final velocity of dolly

v2f = final velocity of statue

Using the conservation of momentum

m v1i + M v2i = m v1f + M v2f

(235)(1) + (233)(0.229) = (235) v1f + (233) v2f

v1f = (288.4 - (233) v2f )/(235)                                              Eq-1

Using conservation of kinetic energy

m v21i + M v22i = m v21f + M v22f

(235)(1)2 + (233)(0.229)2 = (235) v21f + (233) v22f

Using Eq-1

(235)(1)2 + (233)(0.229)2 = (235) ((288.4 - (233) v2f )/(235))2 + (233) v22f

v2f = 1.003 m/s

Using Eq-1

v1f = (288.4 - (233) v2f )/(235) = (288.4 - (233) (1.003))/(235)

v1f = 0.233 m/s

b)

m = mass of dolly = 2 + 233 = 235 kg

v1i = initial velocity of dolly = 1 m/s

M = mass of statue = 233 kg

v2i = initial velocity of statue = 0.229 m/s

v1f = final velocity of dolly

v2f = final velocity of statue

Using the conservation of momentum

m v1i + M v2i = m v1f + M v2f

(235)(1) + (233)(0.229) = (235) v1f + (233) v2f

v1f = (288.4 - (233) v2f )/(235)                                              Eq-1

Using conservation of kinetic energy

(0.80) (m v21i + M v22i) = m v21f + M v22f

(0.80) ((235)(1)2 + (233)(0.229)2) = (235) v21f + (233) v22f

Using Eq-1

197.78= (235) ((288.4 - (233) v2f )/(235))2 + (233) v22f

v2f = 0.824 m/s

Using Eq-1

v1f = (288.4 - (233) v2f )/(235) = (288.4 - (233) (0.824 ))/(235)

v1f = 0.41 m/s