Why is Friction in the Direction of Velocity in this Problem?

[whitehorsey]

1. A package of mass m is dropped vertically onto a horizontal conveyor belt whose speed is v = 1.1 m/s, and the coefficient of kinetic friction between the package and the belt is μ_k = 0.60. For how much time does the package slide on the belt (until it is at rest relative to the belt)?


2. Sum of all the forces = ma


3. Free body diagram:

The picture is the book answer. I drew a similar diagram except with Ff in the opposite direction. Why is F_fr in the direction of velocity for this problem? Compared to a problem where a child is on a slide, friction is on the opposite direction of the child's motion. I always thought that friction was suppose to be on the opposite direction of motion.

 

[SammyS]

1. A package of mass m is dropped vertically onto a horizontal conveyor belt whose speed is v = 1.1 m/s, and the coefficient of kinetic friction between the package and the belt is μ_k = 0.60. For how much time does the package slide on the belt (until it is at rest relative to the belt)?

2. Sum of all the forces = ma

3. Free body diagram:
View attachment 58776

The picture is the book answer. I drew a similar diagram except with Ff in the opposite direction. Why is F_fr in the direction of velocity for this problem? Compared to a problem where a child is on a slide, friction is on the opposite direction of the child's motion. I always thought that friction was suppose to be on the opposite direction of motion.

Did your course give you some definition(s) of frictional force? I'm not referring to $\ F_\text{Friction}=\mu\,N\,,\$ which just gives you the magnitude of the force of friction ?

 

[ehild]

The picture is the book answer. I drew a similar diagram except with Ff in the opposite direction. Why is F_fr in the direction of velocity for this problem? Compared to a problem where a child is on a slide, friction is on the opposite direction of the child's motion. I always thought that friction was suppose to be on the opposite direction of motion.

Friction always opposes relative motion between surfaces in contact. The package has backward relative velocity with respect to the belt, as the belt moves forward, and initially the package was in rest with respect to the ground. The friction opposes that relative motion, so it accelerates the package forward till it moves together wit the belt. The child on a slide moves with respect to the ice (which is in rest) so friction is against the motion of the slide: it points backwards with respect its velocity.

ehild

 

[whitehorsey]

Did your course give you some definition(s) of frictional force? I'm not referring to $\ F_\text{Friction}=\mu\,N\,,\$ which just gives you the magnitude of the force of friction ?

The definition we got was when an object is in motion on a surface there will be a resistance to the motion.

Friction always opposes relative motion between surfaces in contact. The package has backward relative velocity with respect to the belt, as the belt moves forward, and initially the package was in rest with respect to the ground. The friction opposes that relative motion, so it accelerates the package forward till it moves together wit the belt. The child on a slide moves with respect to the ice (which is in rest) so friction is against the motion of the slide: it points backwards with respect its velocity.

ehild

How did you know the package has backward relative velocity?

I'm also confused about how you knew that friction is opposing the velocity of the box and the velocity of the slide instead of the conveyor belt and the child?

 

[ehild]

How did you know the package has backward relative velocity?

The package is dropped onto the belt. That means it was initiall in rest with respect to the ground. Its horizontal velocity stays zero when it reaches the belt, which moves forward. So the package moves backwards with respect to the belt.
If you look out of a train, you see the outside trees, buildings moving backwards...

I'm also confused about how you knew that friction is opposing the velocity of the box and the velocity of the slide instead of the conveyor belt and the child?

The friction is a force of interaction. It means forces of equal magnitude and opposite directions (Newton's Third Law) on both parts and opposes their motion relative to each other.

The frictional force from the belt accelerates the package, and the friction from the package tries to decelerate the belt.

The friction from the ground decelerates the slide, the force of friction from the slide tries to accelerate the Earth.

ehild

 

[SammyS]

The definition we got was when an object is in motion on a surface there will be a resistance to the motion.

Yes, the direction of the force of friction is in a direction which opposes the relative motion of the objects.

How did you know the package has backward relative velocity?

I'm also confused about how you knew that friction is opposing the velocity of the box and the velocity of the slide instead of the conveyor belt ...

Looking at it this way may help.

The conveyor belt is moving to the right relative to the box, therefore, the box will exert a friction force on the conveyor belt which is to the left.

If the box exerts a force on the conveyor which is to the left, then the conveyor belt exerts a (frictional) force on the box which is to the right.

It also should be pretty clear that the conveyor makes the box accelerate to the right. The only force present which is in a horizontal direction is friction. Therefore, the conveyor belt exerts a force (friction) on the box, the direction of which is to the right.

 

[whitehorsey]

Thanks you guys!