Three Students (Teresa, 50 0 Kg. Sara, 60 0Kg. and Doug. 80 kg) decide to go rol

Question

Three Students (Teresa, 50 0 Kg. Sara, 60 0Kg. and Doug. 80 kg) decide to go roller rink instead of studying physics In order to salve their consciences, they perform a quick experiment at the rink. While standing close together in a small circle each student presses the palms of his or her hands against those other two students. Then they simultaneously push off from each other. Doug rolls off at 0.650 m/s directly toward the seats Sara moves away at 0.500 rn/s at an angle of 110 degree anticlockwise from Doug's line of motion as shown in the figure below. How fast and in what direction is Teresa pushed? Find the magnitude of momentums for each person Find the kinetics energy of each person

Explanation / Answer

T = 50.0 Kg
S = 60.0 Kg
D = 80.0 Kg

Vd = 0.650 m/s
Vs = 0.50 m/s
Vt = ?

(a)
Using Momentum Conservation
Initial Momentum = Final Momentum

In x Direction,
D*Vd = S*Vs*sin(20) + T*Vt * sin()
80.0 * 0.650 = 60.0 * 0.50*sin(20) + 50.0 * Vt * sin()
Vt * sin() = 0.835 -------1

In y Direction,
S*Vs*cos(20) + T*Vt * cos() = 0
Vt * cos() =  60/50 * 0.50*cos(20)
Vt * cos() = 0.564 ---------2

Dividing eq 1/2
tan() = 0.835/0.564
= 56o

Vt = 0.564/cos(56)
Vt = 1.00 m/s

Speed of Theresa, Vt = 1.00 m/s
Direction = 146 o Clockwise from Doug's line of motion.

(b)

Magnitude of Momentum of each person are as below,

Momentum of Doug, = 80.0 * 0.650 Kgm/s
Momentum of Doug, = 52 Kg m/s

Momentum of Sara, = 60.0 * 0.50 Kgm/s
Momentum of Sara, = 30 Kg m/s

Momentum of Teresa, = 50.0 * 1.0 Kgm/s
Momentum of Teresa, = 50.0 Kg m/s

(c)
Kinetic Energy of Each person,


Kinetic Energy of Doug, = 1/2 * 80.0 * 0.650^2 J
Kinetic Energy of Doug, = 16.9 J

Kinetic Energy of Sara, = 1/2 *60.0 * 0.50^2 J
Kinetic Energy of Sara, = 7.5 J

Kinetic Energy of Teresa, = 1/2 *50.0 * 1.0^2 J
Kinetic Energy of Teresa, = 25 J

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