Identical twins, each with mass 61.4 kg, are on ice skates and at rest on a froz

Question

Identical twins, each with mass 61.4 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 3.00 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B? Twin Am/s Twin B m/s Need Help? Read it to a 8, ,-/2 points SeCP97.P003.son. + Ask Your The tires on a new compact car have a diameter of 2.0 ft and are warranted for 59,000 miles. (a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. (b) How many revolutions of the tire are equivalent to your answer in (a)? rev Need Help? to a 9. 2/2 points I 7 P.004 soln A potter's wheel moves uniformly from rest to an angular speed of 0.24 rev/s in 25.0 s

Explanation / Answer

Apply conservation of momentumthe fi rst event (twin A tossing the pack), taking the direction
of the velocity given the backpack as positive.

mA vAf + m_puck v_pack = ( m_A+ m_pack) (0) = 0

v_Af = - m_pack v_pack/ m_A

= - 12(3)/61.4

=-0.586 m/s

Conservation of momentum when twin B catches and holds onto the backpack yields

(m_b+ m_pack) v_Bf = m_B(0) + m_pack v_pack

v_Bf = m_pack v_pack/m_B + m_pack

= 12 kg ( 3) / 61.4+12

=0.490 m/s

(b)

theta = s/r = 59000 mi/1ft * ( 5280 ft/ mi)

=3.11 * 10^8 rad

n = s/ 2pi r

= 59000 miles / 2 pi ( 1 ft) * ( 5280 ft/ 1 mi)

=49579947 rev  

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