A penguin stands on the left edge of a sled which is resting on frictionless ice

Question

A penguin stands on the left edge of a sled which is resting on frictionless ice. The penguin and the sled have equal masses. The coordinate systems in the lab frame and in the sled frame are shown. The zero position of the sled frame is at the left end of the sled. For each of the statements below, select the correct answer from the table: The penguin walks to the right edge of the sled. Where is the origin of the sled frame, as measured in the lab frame? The penguin walks to the right edge of the sled. Where is the centre of mass of the sled plus penguin system in the lab frame? The penguin does not move. Where is the centre of mass of the sled plus penguin in the sled frame? The penguin does not move. Where is the centre of mass of the sled in the sled frame? The penguin walks to the right edge of the sled. Where is the centre of mass of the sled plus penguin system in the sled frame? The penguin walks to the right edge of the sled. How far does the penguin move in the lab frame?

Explanation / Answer

1.

when the penguin is at left side

Xcm = m x 0 + m (L/2) / (m + m) = L/4

let the sled moves a distance "d" towards right

Xcm = m (L + d) + m (L/2 + d) / (m + m)

2mL/4 = 3mL/2 + 2md

-mL = 2md

d= - L/2

hence the center of sled moves left by L/2

location of origin of sled = 0

2.

location of center of mass of sled + penguin = L/4

3.

when the penguin is at left side

Xcm = m x 0 + m (L/2) / (m + m) = L/4

4.

L/2

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