Fn = m x g
Fn = 5 kg x 10 m/s^2
Fn = 50 kg m/s^2
Plug in the values of Fn in the formula:
Ff = μ x Fn
Ff = 0.5 x 50 kg m/s^2
Ff = 25 kg m/s^2 or Ff = 25 N

Introduction:
The coefficient of friction is a measure of the resistance between two surfaces in contact. In this scenario, we have a block of mass 5kg that is in contact with a wall. We are asked to find the minimum force required to hold the block against the wall, given that the coefficient of friction between the block and the wall is 0.5.

Understanding the problem:
To solve this problem, we need to consider the forces acting on the block and the conditions required for equilibrium. The block is in contact with the wall, and there are two types of forces acting on it - the force of gravity pulling the block downwards (weight) and the force of friction between the block and the wall.

Determining the force of friction:
The force of friction can be calculated using the formula:

F_friction = μN

where F_friction is the force of friction, μ is the coefficient of friction, and N is the normal force.

In this case, the normal force is equal to the weight of the block, which can be calculated using the formula:

N = mg

where N is the normal force, m is the mass of the block, and g is the acceleration due to gravity (approximately 9.8 m/s²).

So, the force of friction can be calculated as:

F_friction = μN = μmg

Determining the minimum force:
To determine the minimum force required to hold the block against the wall, we need to consider the conditions for equilibrium. In equilibrium, the net force on the block is zero. Therefore, the force of friction must be equal to the force applied on the block to hold it against the wall.

So, the minimum force required, F, can be calculated as:

F = F_friction = μmg

Substituting the given values into the equation:

F = (0.5)(5kg)(9.8m/s²) = 24.5N

Therefore, the minimum force required to hold the block against the wall is 24.5N.

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