An object (mass 3.2kg ) slides upward on a vertical wall at constant velocity when a force F of 54N acts on it at an angle of 60∘ to the horizontal. N = 27 N

Determine the force of kinetic friction on the object.

F(fr) +mg= F(y)

F(y) = Fsinα
F(fr) =Fsinα-mg

To determine the force of kinetic friction on the object, we need to find the net force acting on it.

Given:
Mass of the object, m = 3.2 kg
Force applied, F = 54 N
Angle of the force with the horizontal, θ = 60°
Normal force, N = 27 N

First, let's find the vertical component of the applied force:
Vertical Component of F = F * sin(θ)
= 54 N * sin(60°)
= 54 N * 0.866
≈ 46.71 N

Since the object is sliding upward at a constant velocity, the net force in the vertical direction is zero:
Net Force (in the vertical direction) = Force of gravity - Vertical Component of F - Force of kinetic friction

The force of gravity can be calculated using the equation:
Force of gravity = mass * acceleration due to gravity
= m * g

where acceleration due to gravity, g ≈ 9.8 m/s^2.

Force of gravity = 3.2 kg * 9.8 m/s^2
≈ 31.36 N

Now, rearranging the formula for net force in the vertical direction, we have:
Force of kinetic friction = Force of gravity - Vertical Component of F
= 31.36 N - 46.71 N
≈ -15.35 N

The negative sign indicates that the force of kinetic friction is acting in the opposite direction of motion.

Therefore, the force of kinetic friction on the object is approximately 15.35 N in the downward direction.

To determine the force of kinetic friction on the object, we need to consider the forces acting on it. In this case, we have the force applied to the object (F = 54N) and the normal force (N = 27N) acting perpendicular to the wall. The kinetic friction force opposes the motion of the object, so it acts in the opposite direction to the force applied.

First, we need to calculate the vertical component of the force applied. Since the force is at an angle of 60∘ to the horizontal, we can use trigonometry to determine the vertical component:

Vertical component of force = Force applied × sin(60∘)
= 54N × sin(60∘)

Next, we calculate the net force acting vertically by considering the forces in the vertical direction:

Net force vertically = Force applied vertically - Weight of the object
= Vertical component of force - Weight of the object

The weight of an object is given by the equation:

Weight = mass × gravitational acceleration
= mass × g

Where g is the acceleration due to gravity (approximately 9.8 m/s²).

Weight of the object = mass × g
= 3.2kg × 9.8 m/s²

Substituting the given values, we get:

Weight of the object = 3.2kg × 9.8 m/s²

Finally, we can calculate the net force vertically by substituting the values back into the equation:

Net force vertically = Vertical component of force - Weight of the object

Once we have this value, the force of kinetic friction on the object is equal to the net force vertically acting in the opposite direction.