Consider the situation shown in figure. The strings are massless and pulley is fixed and frictionless. The speed of 3 kg mass just before touching the ground is (g = 10 m s-²)

To determine the speed of the 3 kg mass just before it touches the ground, we can apply the principles of energy conservation or kinematics. Since the strings are massless and the pulley is fixed and frictionless, we can simplify our calculations significantly. Let’s break this down step by step.

Understanding the Scenario

In this situation, we have a mass (m) of 3 kg that is likely being dropped from a certain height (h). The gravitational force acting on it will cause it to accelerate downwards. We can use the equations of motion or energy conservation to find the final speed just before it hits the ground.

Using Kinematics

If we know the height from which the mass is dropped, we can use the kinematic equation:

• v² = u² + 2as

Where:

• v = final velocity (what we want to find)
• u = initial velocity (0 m/s, since it starts from rest)
• a = acceleration due to gravity (10 m/s²)
• s = distance fallen (height h)

Calculating Final Velocity

Assuming the mass falls from a height of h meters, the equation simplifies to:

• v² = 0 + 2 * 10 * h
• v² = 20h

To find the final speed (v), we take the square root:

• v = √(20h)

Using Energy Conservation

Alternatively, we can use the principle of conservation of mechanical energy. The potential energy (PE) at the height will convert to kinetic energy (KE) just before it hits the ground:

• PE = KE

Potential energy is given by:

• PE = mgh

Kinetic energy is given by:

• KE = (1/2)mv²

Setting these equal gives:

• mgh = (1/2)mv²

We can cancel the mass (m) from both sides (as long as it’s not zero):

• gh = (1/2)v²

Rearranging this to find v gives:

• v² = 2gh

Taking the square root results in:

• v = √(2gh)

Final Calculation

Now, substituting g = 10 m/s² into either formula, we can find the speed just before the mass hits the ground:

• v = √(20h) or v = √(20h)

To find the exact speed, we need the height (h) from which the mass is dropped. If you provide that height, we can calculate the final speed numerically.