How Far Will a Sliding Box Travel After Leaving a Ramp?

[DocDaGeniouss]

A box with no mass given is sliding down a ramp and the degree angle is 28. The ramp is two meters long. When the ramp ends there is a 1.0m table that connects to the ramp. After the table it just drops 1.2 meters to the floor. The friction on the ramp is .33 and .27. The friction on the table is .41 and .36. Part A of the question was to calculate whether the box will move or not. The second part of the problem is to determine whether it will stop sliding across the table or if it will go off the table onto the floor and if so how far away from the table will the box hit the floor

Normal Force = mass x acceleration
Normal force = ffr/u

Since i am not given a mass i substituted x in for the mass. I drew out a free body diagram and i calculated the the force going down the ramp is 4.6x . The friction going up the ramp which is the static is 2.85x . Because the force going down the ramp is greater than the static friction the box will move down the ramp. I then did ax = (4.6-2.85)x to find acceleration and got 1.75m/sec^2. I think that part is right.

Now i need to determine how far the box will go, will it stop on the table, if so where, or will it go off the table onto the floor and if so where. I'm really stumped at this point and I am not sure what to do.

 

[alphysicist]

Hi DocDaGeniouss,

A box with no mass given is sliding down a ramp and the degree angle is 28. The ramp is two meters long. When the ramp ends there is a 1.0m table that connects to the ramp. After the table it just drops 1.2 meters to the floor. The friction on the ramp is .33 and .27. The friction on the table is .41 and .36. Part A of the question was to calculate whether the box will move or not. The second part of the problem is to determine whether it will stop sliding across the table or if it will go off the table onto the floor and if so how far away from the table will the box hit the floor

Normal Force = mass x acceleration
Normal force = ffr/u

Since i am not given a mass i substituted x in for the mass. I drew out a free body diagram and i calculated the the force going down the ramp is 4.6x . The friction going up the ramp which is the static is 2.85x . Because the force going down the ramp is greater than the static friction the box will move down the ramp. I then did ax = (4.6-2.85)x

No, I don't believe that is correct. You have already determined the box is moving. So what type of friction is involved?

to find acceleration and got 1.75m/sec^2. I think that part is right.

Now i need to determine how far the box will go, will it stop on the table, if so where, or will it go off the table onto the floor and if so where. I'm really stumped at this point and I am not sure what to do.

The box will stop if the frictional force from the table is strong enough to stop it in in 1m. You can find the acceleration that is caused by the frictional force. Can you find its velocity at the moment it reaches the table (right after it has left the ramp)? With that you can find the distance required for friction to stop the box, and then compare that with 1 m.

If you find that it doesn't have room to stop, then you can treat the rest of the problem as a projectile problem.