A sling shot accelerated a 12g stone to a velocity of 35m/s within a distance of 5.0cm. To what (constant) force is the stone subjected during the acceleration?

To determine the constant force acting on the stone during its acceleration, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). However, we first need to calculate the acceleration of the stone. We can find acceleration using the kinematic equation that relates initial velocity, final velocity, distance, and acceleration.

Step 1: Identify the Variables

In this scenario, we have the following information:

• Mass of the stone (m): 12 g (which we need to convert to kilograms)
• Final velocity (v): 35 m/s
• Initial velocity (u): 0 m/s (the stone starts from rest)
• Distance (s): 5.0 cm (which we need to convert to meters)

Step 2: Convert Units

First, let's convert the mass from grams to kilograms and the distance from centimeters to meters:

• Mass: 12 g = 0.012 kg
• Distance: 5.0 cm = 0.05 m

Step 3: Calculate Acceleration

We can use the kinematic equation:

v² = u² + 2as

Substituting the known values:

(35 m/s)² = (0 m/s)² + 2a(0.05 m)

This simplifies to:

1225 = 0 + 0.1a

Now, solving for acceleration (a):

a = 1225 / 0.1 = 12250 m/s²

Step 4: Calculate the Force

Now that we have the acceleration, we can find the force using Newton's second law:

F = ma

Substituting the values we have:

F = 0.012 kg * 12250 m/s²

Calculating this gives:

F = 0.147 kg·m/s² = 0.147 N

Final Result

The constant force to which the stone is subjected during its acceleration is approximately 0.147 Newtons.

This example illustrates how we can apply basic physics principles to solve real-world problems. By breaking down the problem into manageable steps, we can systematically find the answer while reinforcing our understanding of the concepts involved.