Question

While chopping down his father's cherry tree, George discovered that if he swung the axe with a speed of 25 m/s, it would embed itself 2.3 cm into the tree before coming to a stop. a) If the axe head had a mass of 2.5 kg, how much force was the tree exerting on the axe head upon impact? b) How much force did the axe exert back on the tree?

Answer 1

a) The force exerted on the axe head by the tree is approximately 160,870 N. b) The force exerted by the axe back on the tree is also approximately 160,870 N.

Step-by-step explanation:

In order to answer this question, we need to use the equation F = ma, where F is the force, m is the mass, and a is the acceleration.

a) To calculate the force exerted on the axe head by the tree upon impact, we can use the equation F = ma. The mass of the axe head is given as 2.5 kg and the speed is 25 m/s. We'll need to convert the 2.3 cm into meters (0.023 m).

Using the formula, F = 2.5 kg x (25 m/s)^2 / 0.023 m, we can determine that the force exerted by the tree on the axe head is approximately 160,870 N.

b) To calculate the force exerted by the axe back on the tree, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Therefore, the force exerted by the axe back on the tree is also approximately 160,870 N.