Math Problem Statement

If a 53 kg boulder falls off a cliff, what is the force with which it will hit the ground? Include units.

Solution

To determine the force with which the 53 kg boulder will hit the ground, we need to use Newton's second law of motion, which states:

F=maF = ma

Where:

  • FF is the force,
  • mm is the mass,
  • aa is the acceleration.

Here, the mass m=53kgm = 53 \, \text{kg}. The acceleration due to gravity a=9.81m/s2a = 9.81 \, \text{m/s}^2 (on Earth).

Now, we calculate the force:

F=53kg×9.81m/s2F = 53 \, \text{kg} \times 9.81 \, \text{m/s}^2

Let's compute that.

F=519.93NF = 519.93 \, \text{N}

So, the force with which the boulder hits the ground is approximately 519.93 N (Newtons).

This value represents the weight of the boulder, which is the force exerted due to gravity. However, the actual force of impact when the boulder hits the ground could be higher, depending on factors like the height of the fall and the nature of the collision (i.e., the duration of impact).

Would you like more details on impact force or any other related concepts?

Follow-up Questions:

  1. How can the height from which the boulder falls affect the impact force?
  2. What other factors determine the impact force when an object hits the ground?
  3. Can air resistance significantly affect the boulder's fall?
  4. How does the force differ between a soft and hard landing surface?
  5. What equations are used to calculate the velocity just before the boulder hits the ground?

Tip:

Always account for all forces acting on an object during free fall, including air resistance, when calculating the actual impact force in real-life scenarios.

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Math Problem Analysis

Mathematical Concepts

Newton's Second Law
Force
Gravity

Formulas

F = ma
F = 53 kg × 9.81 m/s^2

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-12