A,package,crate,is,placed,on,a,20,deg,inclined,plane.If,the,coefficient,of,static,friction,between,the,crate,and,the,plane,is,0.65,Will,the,crate,slide,down,the,plane?,justify,your,answer!
The crate will slide down the plane IF
M g sin 20 > M g cos 20*0.65
sin 20 > 0.65 cos 20
tan 20 > 0.65
Check your trig functions and see if this is true.
since tan20 is 0.36 which is less than 0.65, therefore the crate will not slide.
To determine whether the crate will slide down the inclined plane, we need to compare the force of gravity acting on the crate with the maximum static friction force that can be exerted on the crate.
Steps to find out if the crate will slide down the plane:
1. Calculate the force of gravity acting on the crate:
The force of gravity can be calculated using the formula:
Force of gravity = mass * acceleration due to gravity
Since the mass of the crate is not given, we cannot calculate the exact force of gravity.
2. Calculate the maximum static friction force:
The maximum static friction force can be calculated using the formula:
Maximum static friction force = coefficient of static friction * normal force
The normal force can be calculated using the formula:
Normal force = mass * acceleration due to gravity * cos(theta)
(where theta is the angle of inclination, which is mentioned as 20 degrees in the question)
However, since the mass of the crate is not given, we cannot calculate the exact maximum static friction force.
3. Compare the force of gravity with the maximum static friction force:
If the force of gravity is greater than the maximum static friction force, the crate will slide down the plane. Otherwise, it will not slide.
Since the mass of the crate is not given, it is not possible to determine the exact values of the force of gravity and the maximum static friction force to make a direct comparison. Therefore, without the mass of the crate or any other information, we cannot definitively determine whether the crate will slide down the inclined plane or not.
To determine whether the crate will slide down the inclined plane, we need to compare the force of gravity pulling the crate down the plane (parallel to the incline) with the force of static friction trying to hold the crate in place. If the force of gravity exceeds the force of static friction, the crate will slide down the plane.
To calculate the force of gravity, you need to know the weight of the crate. Let's assume the crate weighs 100 Newtons (N).
The force of gravity acting on the crate parallel to the incline can be calculated using the formula:
Force of gravity (parallel to the incline) = weight of the crate * sin(theta)
Here, theta represents the angle of the inclined plane, which is 20 degrees.
Using the formula:
Force of gravity (parallel to the incline) = 100 N * sin(20 degrees)
Calculating sin(20 degrees) = 0.3420, so:
Force of gravity (parallel to the incline) = 100 N * 0.3420 = 34.2 N
Next, we need to calculate the force of static friction. The force of static friction can be determined using the formula:
Force of static friction = coefficient of static friction * normal force
The normal force acting on the crate is the force perpendicular to the incline. It can be calculated using the formula:
Normal force = weight of the crate * cos(theta)
Using the values:
Normal force = 100 N * cos(20 degrees)
Calculating cos(20 degrees) = 0.9397, so:
Normal force = 100 N * 0.9397 = 93.97 N
Now, let's calculate the force of static friction using the coefficient of static friction, which is given as 0.65:
Force of static friction = 0.65 * 93.97 N
Force of static friction = 60.88 N
Since the force of gravity (34.2 N) is less than the force of static friction (60.88 N), the crate will not slide down the plane. The static friction force is greater than the force of gravity, so the crate will remain in place on the inclined plane.
Therefore, the crate will not slide down the inclined plane in this scenario.