HELP!!!
A box rest on an incline making a 34 angle with the horizontal. It is found that a parallel force to the incline of at least 240 N can prevent the box from sliding down the incline. If the weight of the box is 800 N, find the coefficient of static friction between the box and the incline.
weight component down = m g cos 34
friction force up = m g cos 34 * mu
so
mu m g cos 34 + 240 = m g sin 34
I get 8.01. That doesn't seem correct. I plugged in all my numbers. Anything you think I could have done incorrectly?
I converted newtons to kilograms and my answer makes more sense to me. I got 0.312 for mu this time. Thank you for the guidance.
M*g = 800 N.
Fp = 800*sin34 = 447.4 N.
Fn = 800*Cos34 = 663.2 N.
Fap-Fp-Fs = M*a.
240-447.4 + Fs = M*0 = 0
Fs = 207.4 N. = Force of static friction.
u = Fs/Fn = 207.4/663.2 = 0.313.
To find the coefficient of static friction between the box and the incline, we need to use the concept of equilibrium and the force components acting on the box.
Let's break down the forces acting on the box:
1. Weight (W): This is the force due to the gravitational pull acting vertically downward. The weight is given as 800 N.
2. Normal Force (N): This is the perpendicular force exerted by the incline on the box. It acts perpendicular to the incline. In this case, the normal force is equal to the force component of the weight acting along the incline. We can calculate it using the equation: N = W * cos(theta), where theta is the angle of inclination.
3. Force of Gravity Parallel to the Incline (W_parallel): This force acts parallel to the incline and tends to pull the box down the incline. We can calculate it using the equation: W_parallel = W * sin(theta), where theta is the angle of inclination.
4. Force of Static Friction (F_static): This force acts parallel to the incline in the opposite direction to the force of gravity parallel to the incline. The force of static friction helps prevent the box from sliding down the incline.
According to the given information, a parallel force of at least 240 N is required to prevent the box from sliding down. Since this force of 240 N is equal to the force of static friction, we can write the equation: F_static = 240 N.
Now, we can set up the equation of equilibrium:
Sum of forces along the x-axis = 0
F_static + W_parallel = 0
Since W_parallel = W * sin(theta), we can substitute it into the equation:
F_static + W * sin(theta) = 0
Substituting the known values:
240 N + 800 N * sin(34°) = 0
Now, we can solve for sin(34°) and find the coefficient of static friction:
240 N = -800 N * sin(34°) [Multiplying by -1 to isolate the sin(34°) term.]
sin(34°) = 240 N / -800 N
sin(34°) = -0.3
To find the coefficient of static friction, we can use the equation:
coefficient of static friction (μ) = |sin(34°)|
Therefore, the coefficient of static friction between the box and the incline is 0.3.