Question

a 2.0 kg bag is held by a string to the ceiling. a 10.0 g bullet travelling at 100. m/s strikes the bag. the speed of the bag after the collision is 0.80 m/s. assuming there is no friction, determine the maximum height of the bag after the collision.

Answer 1

To find the maximum height the bag reaches after being struck by a bullet, we apply the principle of conservation of energy. After calculating the initial kinetic energy, we equate it to the potential energy at the maximum height, yielding a height of approximately 0.03265 meters.

Step-by-step explanation:

To determine the maximum height the bag reaches after the collision, we must first use the principle of conservation of momentum to find the velocity of the bag just after the bullet embeds into it. However, since this information is already given (0.80 m/s), we can proceed to find the maximum height using energy conservation principles. The initial kinetic energy of the bag-bullet system after the collision will transform into gravitational potential energy at the maximum height.

The kinetic energy just after the collision is KE = (1/2)m(v^2), where m is the mass of the bag plus the bullet, and v is the speed after the collision. The gravitational potential energy at the maximum height is PE = mgh, where g is the acceleration due to gravity (9.8 m/s2), and h is the height above the lowest point.

Setting the kinetic energy equal to the potential energy allows us to solve for the height:
(1/2)m(v2) = mgh. Solving for h gives us the equation h = (v2) / (2g). Plugging in the values, we get the maximum height h = ((0.80 m/s)2) / (2 * 9.8 m/s2) = 0.03265 meters.