Frictional force on a ladder leaning against a wall

Explanation:
When a ladder is resting on a smooth ground and leaning against a vertical wall, the force of friction acting on the ladder is given by:

F friction = μR

where μ is the coefficient of friction between the ladder and the ground, and R is the normal reaction force acting on the ladder.

Now, let's consider the forces acting on the ladder:

1. Weight of the ladder (W): Vertical force acting downwards at the center of mass of the ladder.

2. Normal reaction force (R): Force acting perpendicular to the ground at the point of contact between the ladder and the ground.

3. Frictional force (F friction): Force acting parallel to the ground and in the opposite direction to the motion of the ladder.

4. Force due to the wall (F wall): Force acting perpendicular to the wall at the point of contact between the ladder and the wall.

Since the ladder is in equilibrium, the sum of all the forces acting on it must be zero. Therefore,

ΣF = W + R + F friction + F wall = 0

Now, let's consider the forces acting on the upper end of the ladder:

1. Weight of the ladder (W): Vertical force acting downwards at the upper end of the ladder.

2. Normal reaction force (R): Force acting perpendicular to the wall at the upper end of the ladder.

3. Frictional force (F friction): Force acting parallel to the ground and in the opposite direction to the motion of the ladder, at the upper end of the ladder.

4. Force due to the wall (F wall): Force acting perpendicular to the wall at the upper end of the ladder.

Since the ladder is in equilibrium, the sum of all the forces acting on the upper end of the ladder must be zero. Therefore,

ΣF upper end = W + R + F friction + F wall = 0

Now, let's analyze the direction of the frictional force:

1. The ladder is leaning against the wall, which means that the force due to the wall (F wall) is acting towards the wall.

2. The ladder is not moving, which means that the frictional force (F friction) is equal and opposite to the horizontal component of the force due to the wall (F wall).

3. Therefore, the frictional force (F friction) is acting upwards at the upper end of the ladder, in order to balance the horizontal component of the force due to the wall (F wall) and keep the ladder in equilibrium.

Hence, the correct answer is option 'C' - upwards at its upper end.