Respuesta :
To prevent the crate from slipping, the maximum force that the belt can exert on the crate must be equal to the static friction force.
Ff = 0.5 * 16 * 9.8 = 78.4 N
a = 4.9 m/s^2
If acceleration of the belt exceeds the value determined in the previous question, what is the acceleration of the crate?
In this situation, the kinetic friction force is causing the crate to decelerate. So the net force on the crate is 78.4 N minus the kinetic friction force.
Ff = 0.28 * 16 * 9.8 = 43.904 N
Net force = 78.4 – 43.904 = 34.496 N
To determine the acceleration, divide by the mass of the crate.
a = 34.496 ÷ 16 = 2.156 m/s^2
The maximum acceleration for the belt that the slipping of the crate does not appear is 2 m/s².
What is friction?
Friction is the force that resists the motion of a body when the body is in contact with another body or surface.
The friction force of a body is the product of the normal force acting on the body and the coefficient of the friction of that body. It can be given as,
[tex]F_f=\mu F_n[/tex]
Here, [tex]F_n[/tex] is the normal force and [tex]\mu[/tex] is the coefficient of the friction.
The normal force acting on a body is a product of mass times acceleration (gravitational for the given case). Thus the above formula can be written as,
[tex]F_f=\mu mg[/tex]
The mass of the crate is 10 kg and the coefficient of the static friction is 0.5. Thus, find the static friction force by putting the values in the above formula as,
[tex]F_s=0.5\times10\times9.8\\F_s=49\rm N[/tex]
The mass of the crate is 10 kg and the coefficient of the kinetic friction is 0.3. Thus, find the kinetic friction force by putting the values in the above formula as,
[tex]F_k=0.3\times10\times9.8\\F_s=49\rm N\\F_k=29.4\rm N[/tex]
Now, the net force acting on the body is,
[tex]F=F_s-F_k\\F=49-29.4\\F=19.6\rm N[/tex]
As, the maximum acceleration is the ratio of the net force acting to the mass of the object. Thus, the maximum acceleration the belt can have without the crate slipping is,
[tex]a=\dfrac{19.6}{10}\\a=1.96\rm m/s^2\\a\cong2 m/s^2[/tex]
Thus, the maximum acceleration for the belt that the slipping of the crate does not appear is 2 m/s².
Learn more about the friction force here;
https://brainly.com/question/13680415
