Question

A small 13.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 70.0 g and is 120 cm in length. The bug jumps off in the horizontal direction, perpendicular to the bar, with a speed of 25.0 cm/s relative to the table.

Answer 1

The speed of the bar relative to the table when the bug jumps off is 4.64 cm/s.

The given parameters;

• mass of the bug, m₁ = 13 g = 0.013 kg
• mass of the bar, m₂ = 70 g = 0.07 kg
• speed of the bug, u₁ = 25 cm/s = 0.25 m/s

The final speed of the bar relative to the table can be determined by applying the principle of conservation of linear momentum as shown below;

m₁u₁ = m₂u₂

$u_2 = \frac{m_1 u_1}{m_2} \\\\u_2 = \frac{(0.25 \times 0.013)}{0.07} \\\\u_2 = 0.0464 \ m/s\\\\u_2 = 4.64 \ cm/s$

Thus, the speed of the bar relative to the table when the bug jumps off is 4.64 cm/s.

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