Physics Challenge: Calculating Force on a Palm Tree

How can we calculate the force on a palm tree when hit by a ball?

You have just planted a sturdy 2-m-tall palm tree in your front lawn for your mother’s birthday. Your brother kicks a 500 g ball, which hits the top of the tree at a speed of 5 m/s and stays in contact with it for 10 ms. The ball falls to the ground near the base of the tree and the recoil of the tree is minimal. What is the force on the tree?

Calculating Force on a Palm Tree

The force on the tree which is exerted by the ball that hits it is calculated using the impulse principle in physics. Impulse is the change in momentum of an object when a force is applied over a period of time. Given the ball's mass, initial velocity, and the contact time, the force on the tree can be calculated as -250 N.

Understanding the Calculation

Here we're talking about an elastic collision in which an object (in this case a ball) hits another object (the tree). In your scenario, the object is hitting the tree and exerting a force. This can be understood using the concept of impulse in physics, which is the change in momentum of an object when a force is applied over a period of time.

Impulse (J) is calculated as the Force (F) × Time (t), where force is in Newtons and time is in seconds. To find the Force exerted by the ball on the tree we can rearrange the equation: F = m * Δv / Δt, where:

• m is the mass of the ball (0.5 kg)
• Δv is the change in velocity (final velocity - initial velocity; since the ball comes to rest after hitting the tree, final velocity is 0, therefore Δv is -5 m/s)
• Δt is the time the ball was in contact with the tree (0.01 s)

So, substituting these values in the formula, we get:

F = (0.5 kg * -5 m/s) / 0.01 s = -250 N, the negative sign indicates that the force is exerted downwards.