A 13.0 -kg box is released on a 33 degree incline and accelerates down the incline at 0.20 m/s^2
Find the friction force impeding its motion?
Can someone please take me through this problem step by step? Thank you so very much
ma=mgsinα - F(fr)
F(fr) =m(gsinα –a)
Wb = m*g = 13kg * 9.8N/kg = 127.4 N. =
Wt. of box.
Fb = 127.4N @ 33 Deg.
Fp = 127.4*s.n33 = 69.4 N. = Force parallel to the incline.
Fv = 127.4*cos33 = 106.8 N. = Force perpendicular to plane.
Fn = Fp - Fk = m*a
69.4 - Fk = 13*0.20 = 2.6
-Fk = 2.6 - 69.4 = -66.8
Fk = 66.8 = Force of kinetic energy.
Sure! Let's break down the problem step by step to find the friction force impeding the motion of the box.
Step 1: Identify the given information:
- Mass of the box (m): 13.0 kg
- Acceleration down the incline (a): 0.20 m/s^2
- Angle of the incline (θ): 33 degrees
Step 2: Resolve the forces acting on the box:
There are two main forces acting on the box:
- The gravitational force (mg), which acts vertically downward.
- The friction force (f), which acts parallel to the incline and opposes the motion of the box.
Step 3: Determine the components of the gravitational force:
Since the incline is at an angle (θ), we need to find the components of the gravitational force acting parallel and perpendicular to the incline. The component parallel to the incline is given by mg*sin(θ), and the component perpendicular to the incline is mg*cos(θ).
- Component parallel to the incline (mg*sin(θ)):
Gravitational force = mass * acceleration due to gravity
Gravitational force = m * g
Gravitational force parallel to incline = m * g * sin(θ)
- Component perpendicular to the incline (mg*cos(θ)):
Gravitational force perpendicular to incline = m * g * cos(θ)
Step 4: Determine the net force acting on the box parallel to the incline:
Net force parallel to the incline is responsible for the acceleration of the box down the incline. In this case, the net force is equal to the force of friction (f).
Net force parallel to the incline = m * a
Step 5: Determine the force of friction:
Since the net force is equal to the force of friction, we can equate these two values:
m * a = f
So, the force of friction impeding the motion of the box is equal to m * a.
Step 6: Substitute the given values into the equation:
f = m * a
f = 13.0 kg * 0.20 m/s^2
Calculating this gives us the value of the friction force.
I hope this step-by-step explanation helps you solve the problem. If you have any further questions, feel free to ask!