The 2.5-kg head of an ax exerts a force of 80 kN as it penetrates 18 mm into the truck of a tree. The speed of the ax head when it strikes the tree is
Answer (1)
1. Calculate the work done: The work done by the ax head as it penetrates the tree is calculated by multiplying the force it exerts (80,000 N) by the distance it penetrates (0.018 m). This gives us 1,440 J of work done.2. Relate work to kinetic energy: The work done on the tree is equal to the initial kinetic energy of the ax head because the ax comes to a stop after penetrating the tree. Therefore, the initial kinetic energy is also 1,440 J.3. Calculate the speed: We use the formula for kinetic energy, which is KE = 0.5 * mass * speed². Rearranging this formula to solve for speed gives us speed = sqrt(2 * KE / mass). Plugging in the values, we find the speed to be approximately 33.94 m/s.Thus, the speed of the ax head when it strikes the tree is about 33.94 m/s.
