A particle of mass 4kg is suspended from a point A on a vertical wall by means of a light inextensible string of length 130cm.A horizontal force P, is applied to the particle so that it is held in equilibrium a distance of 50cm from the wall. Find the value of P and the tension in the string.

50/130 is the sine of the angle the string makes with the wall. That angle is therefore A = 22.6 degrees. (The string, wall and horizontal form a 5-12-13 right triangle)

Now write horizontal and vertical force balance equations and solve for P and T. (T is the tension)

The vertical equilibrium equation will be:
T cos22.6 = M g
so you can already solve for T.

The horizontal equilbrium equation is
T sin22.5 = P

You finish it.

Can you please sketch the diagram and give a holistic solution?

Please I need the correct solutions to this. Very urgent

Can I get the diagram

To solve this problem, we can use the principles of equilibrium and the concept of moments.

Let's start by drawing a diagram to visualize the situation. We have the particle of mass 4kg suspended from point A on a vertical wall with a string of length 130cm. The particle is held in equilibrium by a horizontal force P, which is applied a distance of 50cm from the wall.

P
_______
| | A
| |
| |
|______|

There are two forces acting on the particle: the tension in the string and the applied force P. Since the particle is in equilibrium, the net force and the net moment about any point will be zero.

First, let's find the value of P. To do this, we need to analyze the vertical forces acting on the particle. Since there is no vertical acceleration (the particle is not moving up or down), the tension in the string must balance the weight of the particle.

The weight of the particle can be calculated using the equation: weight = mass * gravitational acceleration. In this case, the mass of the particle is 4kg and the gravitational acceleration is approximately 9.8 m/s². Therefore, the weight of the particle is 4 kg * 9.8 m/s² = 39.2 N.

Since the tension in the string balances the weight, we have Tension = Weight = 39.2 N.

Next, let's find the value of P. To do this, we need to analyze the horizontal forces acting on the particle. The only horizontal force is the applied force P. Since there is no horizontal acceleration (the particle is not moving left or right), the force P must be equal in magnitude but opposite in direction to the tension in the string.

Therefore, we have P = tension = 39.2 N.

To summarize:
- The value of P, the horizontal force, is 39.2 N.
- The tension in the string is also 39.2 N.

Remember that the solution is based on assuming the equilibrium of forces and moments.