You and your friends are doing physics experiments on a frozen pond that serves
ID: 1485294 • Letter: Y
Question
You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 79.0 kg , is given a push and slides eastward. Abigail, with mass 60.0 kg , is sent sliding northward. They collide, and after the collision Sam is moving at 36.0 north of east with a speed of 7.00 m/s and Abigail is moving at 15.0 south of east with a speed of 10.0 m/s . a)What was the speed of each person before the collision? Sam's speed: b)Abigail's speed: c)By how much did the total kinetic energy of the two people decrease during the collision?
Explanation / Answer
m1 =79 kg , u1y =0
m2 = 60 kg , u2x =0
v1x = 7cos(36) = 5.663
v1y = 7sin(36) = 4.1145
v2x = 10cos(15) = 9.66
v2y =-10sin(15) = - 2.588
From conservation of momentum along x - direction
m1u1x+m2u2x =m1v1x+m1v1y
(79*u1) +0 = (79* 5.663) + (60*9.66) ... (1)
From conservation of momentum along y direction
m1u1y+m2u2y =m1v1y +m2v2y
0 +(60*u2) = (79*4.1154 )-(60*2.588) ...(2)
By solving (1) and (2) we get
a) initila velocity of Sam u1 = 13 m/s
b) initial velcotiy of Abigali u2 = 2.83 m/s
c) Ki = (1/2)m1u1^2 +(1/2)m2u2^2
Ki = (0.5*79*13*13)+(0.5*60*2.83*2.83)
Ki =6915.8 J
Kf = (1/2)m1v1^2 +(1/2)m2v2^2
Kf = (0.5*79*7*7)+(0.5*60*10*10)
Kf =4935.5 J
Lost in total kinetic energy Ki -Kf = (6915.8 ) -(4935.5)
Lost in total kinetic energy =1980.3 J
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