Collisions, Center of Mass & Motion of a System of Particles - - PDF document

Collisions, Center of Mass & Motion of a System of Particles

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One-Dimensional Perfectly Inelastic Collision

From conservation of momentum

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One-Dimensional Elastic Collisions

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Example 1

(a) By what fraction is the kinetic energy of a neutron (mass

an atomic nucleus (mass

fractional decrease in kinetic energy of a neutron when it collides in this way with a lead nucleus, a carbon nucleus, and a hydrogen nucleus.

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Example 1 Solution

(a) By what fraction is the kinetic energy of a neutron (mass

an atomic nucleus (mass

fractional decrease in kinetic energy of a neutron when it collides in this way with a lead nucleus, a carbon nucleus, and a hydrogen nucleus.

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Example 1 Solution (cont’d)

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Center of Mass

system of

particles is defined as

• ✿
• ✁

• ✍

where

is the total mass

in terms of its components

where

where

is a differential element of mass at (x,y,z)

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Example 2

Locate the center of mass of three particles of mass

1.0 kg,

equilateral triangle 1.0 m on a side.

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Example 2 Solution

Locate the center of mass of three particles of mass

1.0 kg,

equilateral triangle 1.0 m on a side. rcm m3 m1 m2

x (m) y (m) 1

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Kinematics of the Center of Mass

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Example 3

An old Chrysler with a mass 2400 kg is moving along a straight stretch of road at 80 km/h. It is followed by a Ford with a mass 1600 kg moving at 60 km/h. How fast is the center of mass of the two cars moving?

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Example 3 Solution

An old Chrysler with a mass 2400 kg is moving along a straight stretch of road at 80 km/h. It is followed by a Ford with a mass 1600 kg moving at 60 km/h. How fast is the center of mass of the two cars moving?

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Dynamics of the Center of Mass

action-reaction pairs and cancel in pairs (Newton’s 3rd law), so we have

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Motion of the Center of Mass

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Example 4

Two skaters, one with a mass 65 kg and the other with mass 40 kg, stand on an ice rink holding a pole of length 10 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they

• meet. How far does the 40 kg skater move?

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Example 4 Solution

Two skaters, one with a mass 65 kg and the other with mass 40 kg, stand on an ice rink holding a pole of length 10 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they

• meet. How far does the 40 kg skater move?

Since the center of mass of the two-skater system does not move, the two skaters will meet at the center of mass

• f the system. If we let the origin be at the initial position
• f the 40 kg skater, we can calculate the position of the

center of mass. This is also the distance the 40 kg skater will move.

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Homework Set 15 - Due Mon. Oct. 18

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