A box of mass 50kg is placed on an inclined plane. When the angle of the plane is increased to 30°, the box begins to slide downward. Calculate the coefficient of statics friction b/w the plane and box . Draw the free body diagram .
M*g = 50 * 9.8 = 490 N. = Wt. of box.
Fp = 490*sin30 = 245 N. = Force parallel with incline.
Fn = 490*Cos30 = 424 N. = Normal force.
Fs = u*Fn = = 424u. = Force of static friction.
Fp-424u = M*a.
245-424u = M*0 = 0, U = ?.
20.6
To calculate the coefficient of static friction between the inclined plane and the box, we need to consider the forces acting on the box. Let's draw the free body diagram of the box on the inclined plane.
Free body diagram:
_________________
| |
| Box |
|_______________|
|‾‾‾‾‾| |
/ | \
Friction Weight
In the free body diagram, we have the following forces:
1. Friction force: acting in the opposite direction to the motion. This force is denoted as "Friction".
2. Weight force: acting vertically downward due to the box's mass and the force of gravity.
This force is denoted as "Weight".
Now, let's analyze the forces and use them to calculate the coefficient of static friction.
1. Friction force: The maximum static friction force is given by the equation:
Friction = μ × Normal force
μ: coefficient of static friction
Normal force: the force perpendicular to the inclined plane, equal to the weight force acting vertically downward.
2. Weight force: The weight force is given by the equation:
Weight = mass × gravity
mass: mass of the box (given as 50 kg)
gravity: acceleration due to gravity (approximately 9.8 m/s^2)
Since the box is just about to slide downward, the force of static friction is at its maximum, which is equal to the weight force acting vertically downward.
Therefore, the coefficient of static friction (μ) can be calculated using the equation:
μ = Friction / Normal force
Since Friction = Weight, we have:
μ = Weight / Normal force
Now, let's calculate the coefficient of static friction.
Weight = mass × gravity
Weight = 50 kg × 9.8 m/s^2
Weight = 490 N
In this case, the normal force is equal to the component of the weight force perpendicular to the inclined plane. Let's find it.
Normal force = Weight × cos(30°)
Normal force = 490 N × cos(30°)
Normal force = 490 N × 0.866
Normal force ≈ 424.74 N
Finally, we can calculate the coefficient of static friction (μ) using the equation:
μ = Weight / Normal force
μ = 490 N / 424.74 N
μ ≈ 1.153
Therefore, the coefficient of static friction (μ) between the inclined plane and the box is approximately 1.153.
To calculate the coefficient of static friction, we first need to draw a free body diagram of the box on the inclined plane.
1. Draw the inclined plane as a straight line inclined at an angle of 30°.
2. Place the box on the plane with its weight acting vertically downwards.
3. Draw the normal force perpendicular to the plane, pushing upwards.
4. Sketch the frictional force acting along the plane, opposing the motion.
Now, let's calculate the coefficient of static friction.
First, determine the weight of the box (force due to gravity):
Weight = mass × acceleration due to gravity
= 50 kg × 9.8 m/s²
= 490 N
Next, resolve the weight into components parallel and perpendicular to the inclined plane:
Weight (parallel to the plane) = Weight × sin θ
= 490 N × sin 30°
= 245 N
Weight (perpendicular to the plane) = Weight × cos θ
= 490 N × cos 30°
= 425 N
On the inclined plane, there are two forces present: the normal force and the force of friction. Since the box is about to slide downward, the force of static friction will be acting at its maximum capacity to oppose that motion.
The frictional force can be calculated using the formula:
Frictional force = coefficient of static friction × normal force
Let's assume the coefficient of static friction as μ. Therefore:
Frictional force = μ × Normal force
= μ × 425 N
As the box is about to slide downward, the frictional force is at its maximum, which is equal to the parallel component of the weight:
245 N = μ × 425 N
Now, solve this equation for the coefficient of static friction:
μ = 245 N / 425 N
μ ≈ 0.576
Therefore, the coefficient of static friction between the inclined plane and the box is approximately 0.576.