A 100 kg box slides with constant velocity down a ramp inclined at 20 degrees, with the horizontal. Find the frictional force acting on the box.

Wb = mg = 100kg * 8.8N/kg = 980 N. = Wt. of box.

Fb = 980N @ 20 Deg. = Force of the box.
Fp = 980*sin20 = 335.2 N. = Force parallel to ramp.
Fv = 980*cos20 = 920.9 N. = Force perpendicular to ramp.

Fk = Force of kinetic frictin.

Fn = Fp - Fk = ma
335.2 - Fk = 100*0.
335.2 - Fk = 0.
Fk = 335.2 N.

To find the frictional force acting on the box, we need to consider the forces acting on the box along the inclined ramp.

First, let's identify the known information:
- Mass of the box (m): 100 kg
- Angle of the ramp (θ): 20 degrees
- The box moves with a constant velocity, which means the net force acting on it is zero.

The forces acting on the box along the ramp are:
1. Weight of the box (Fg): This force acts vertically downward and can be calculated as:
Fg = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s²).

2. Normal force (Fn): This force acts perpendicular to the ramp to balance the component of the weight along the ramp. It can be calculated as:
Fn = m * g * cos(θ)

3. Frictional force (Ff): This force acts parallel to the ramp and opposes the motion of the box. It can be calculated using the equation:
Ff = μ * Fn
where μ is the coefficient of friction.

Since the box is sliding with a constant velocity, the frictional force is equal to the force required to counterbalance the component of the weight along the ramp. Therefore,
Ff = m * g * sin(θ)

Substituting the given values:
Ff = 100 kg * 9.8 m/s² * sin(20 degrees)
Ff ≈ 332.2 N

Hence, the frictional force acting on the box is approximately 332.2 Newtons.

To find the frictional force acting on the box, we need to determine the total force acting in the horizontal direction.

First, let's analyze the forces acting on the box:

1. Gravity (mg): The force of gravity is acting downwards vertically and can be calculated by multiplying the mass (m) of the box by the acceleration due to gravity (g) which is approximately 9.8 m/s².

F_gravity = m * g

2. Normal force (N): The perpendicular force exerted by the ramp on the box. It acts perpendicular to the ramp's surface and can be calculated by taking the component of the gravitational force acting perpendicular to the ramp. In this case, the normal force will be equal in magnitude but opposite in direction to the component of gravity acting in the perpendicular direction.

N = m * g * cos(θ)

Where θ is the angle of inclination of the ramp (20 degrees).

3. Friction force (F_friction): The force acting in the opposite direction of motion, which is what we're trying to determine.

Since the box is sliding with a constant velocity, we know that the net force acting on it is zero. Therefore, the sum of all the forces in the horizontal direction should be equal to zero.

The forces in the horizontal direction are:

- The component of gravity parallel to the ramp: m * g * sin(θ)
- The frictional force in the opposite direction: -F_friction

Since these forces cancel each other out, we can write:

m * g * sin(θ) - F_friction = 0

Rearranging the equation, we find:

F_friction = m * g * sin(θ)

Substituting the given values:

F_friction = 100 kg * 9.8 m/s² * sin(20°)

Calculating this expression gives us the value of the frictional force acting on the box.