three forces p q r keep a body of mass m in equilibrium q and are perpendicular to each other When p is removed the acceleration of mass is

To understand the situation where three forces \( p \), \( q \), and \( r \) keep a body of mass \( m \) in equilibrium, we first need to clarify what equilibrium means in physics. When an object is in equilibrium, the net force acting on it is zero, which means that all the forces balance each other out. In your case, forces \( q \) and \( r \) are perpendicular to each other, and together with force \( p \), they maintain this balance.

Analyzing the Forces

Let's break down the forces acting on the mass \( m \). Since \( q \) and \( r \) are perpendicular, we can visualize them as forming a right triangle. The resultant force \( R \) of these two forces can be calculated using the Pythagorean theorem:

• If \( |q| \) is the magnitude of force \( q \) and \( |r| \) is the magnitude of force \( r \), then the resultant force \( R \) is given by:
• R = √(q² + r²)

Now, since the body is in equilibrium, the force \( p \) must equal this resultant force \( R \) in magnitude but act in the opposite direction. Therefore, we can express this as:

• |p| = R = √(q² + r²)

What Happens When Force p is Removed?

Now, if force \( p \) is removed, the equilibrium is disrupted. The only forces acting on the mass \( m \) will be \( q \) and \( r \). Since these forces are not balanced by \( p \) anymore, we need to determine the net force acting on the mass.

The net force \( F_{net} \) acting on the mass will simply be the resultant of forces \( q \) and \( r \), which we already calculated as \( R \). Therefore, the net force is:

• F_{net} = R = √(q² + r²)

Calculating the Acceleration

According to Newton's second law of motion, the acceleration \( a \) of an object is given by the formula:

• a = F_{net} / m

Substituting the expression for \( F_{net} \) into this equation gives us:

• a = √(q² + r²) / m

This equation tells us that the acceleration of the mass \( m \) will be directly proportional to the resultant of forces \( q \) and \( r \) and inversely proportional to the mass itself. The direction of the acceleration will be in the direction of the resultant force \( R \), which is the vector sum of \( q \) and \( r \).

Visualizing the Situation

To visualize this, imagine a box sitting on a flat surface. Initially, three strings pull on it: one string pulls it to the left (force \( p \)), while the other two pull it up and to the right (forces \( q \) and \( r \)). When you cut the string pulling it to the left, the box will start to accelerate in the direction of the resultant of the two remaining strings, which is diagonally up and to the right.

In summary, when force \( p \) is removed, the mass \( m \) will experience an acceleration determined by the magnitudes of forces \( q \) and \( r \) divided by the mass. This is a classic example of how forces interact and how equilibrium can be disrupted, leading to motion. Understanding these principles is fundamental in physics and helps explain a wide range of phenomena in the physical world.