In a police ballistics test,a 2.00-g bullet suddenly hits and becomes embedded in a 5.00-kg wood block which is hanging from a 1.20-m long string.This causes the block to swing through an arc of 3.50°.What was the speed of the bullet just before it hit the block?

Question

Quizplus · Accepted Answer

The speed of the bullet can be found using the principle of conservation of energy. Initially, the bullet has kinetic energy, and after the collision, the bullet-block system has potential energy at the highest point of the swing. The potential energy at the highest point can be calculated using the change in height (h) which can be found from the arc length and the angle given. The change in height (h) is related to the length of the string (L) and the cosine of the angle (θ) through the relation h = L(1 - cosθ). The potential energy (PE) at the highest point is mgh, where m is the total mass of the bullet-block system, g is the acceleration due to gravity, and h is the height calculated. This potential energy is equal to the initial kinetic energy (KE) of the bullet, which is (1/2)mv^2, where m is the mass of the bullet and v is its velocity. By equating the potential energy to the kinetic energy and solving for v, the initial speed of the bullet can be determined. This approach involves using trigonometry and conservation of energy principles to find the bullet's speed.

In a Police Ballistics Test,a 2