obtain an expression for minimum safe velocity of a car or bike to move Inwell death
Answers
Explanation:
in the death well , the moter cycle rider dont fall because centripetal force is balanced by the normal components and weight.
now we calculate the total force acting on the rider to balance the centripetal force.
At top the velocity of rider is minimum , so we say v=0 at top
so normal component become zero
F(net)=centripetal force
f+mg=centripetal force
here f= normal component
at top f=0
so
mg=centripetal force
mg=mv^2/r
v=(rg)^1/2
v=(25*10)^1/2
v=15.8m/s
hope it help u
Answer:
When the motorcyclist is at the highest point of the death - well, the normal reaction R on the motorcyclist by the ceiling of the chamber acts downwards. His weight mg also act downwards.
Apparently, this thing is pretty old. The Demon Drome Wall of Death has some nice pictures and history of the wall. Strange that it doesn't list the diameter. It only lists the height of 20 feet. The Wikipedia page says that these shows usually have a cylinder ranging in diameter from 6.1 meters to 11 meters. Fine, I will do my calculations for the whole range of Death Walls.
What about the mass of the car? Well, I know this Mazda2 isn't your basic model. However, if I went with that value listed value it would be around 1000 kg. I can't get the speed of the car without knowing the radius of the cylinder. But I can get the angular speed. Here is a plot of the car as it goes around the wall.
This plot is essentially useless except to get the time it takes to go around the wall once. This is right about 2 seconds making the angular velocity about π rad/s (3.14 rad/s). That is all I can get from the video.
The Physics
Probably the first question that people ask is: how does the car stay on the wall? Here is a diagram showing the forces on the car as it goes around.
I understand that a diagram like this can be difficult to come up with. But here are some tips: start with the forces from things that don't have to touch the object you are interested in. In this case, that is only the gravitational force from the Earth. All the other forces are from things that are touching the car and there is only one such object: the wall. Surfaces can push in two ways. They can push parallel to the surface (this is friction) or they can push perpendicular to the surface - we call this the "normal" force (using the geometry definition meaning perpendicular).
Something has to be pushing up on the car. It can only be the wall since the wall is the only thing touching it and it can only be friction since this would be in the direction parallel to the wall. However, the typical model for the frictional force says that it has a magnitude of:
Where μs is called the coefficient of static friction and depends on the two materials (tire and wood). It is static friction (and not kinetic) because the two surfaces are not sliding relative to each other. Oh, and the less than sign is there because the frictional force pushes whatever it can to make the two surfaces NOT slide. But really, the important part is the FN - the normal force. The harder the two surfaces are pushed together the greater the frictional force. So, the wall has to push on the car perpendicular to the surface of the wall.
But wait. What is pushing the car against the wall? Nothing. Yes, nothing. What else could it be? Nothing else is touching the car, right? There are no other long range forces that you could put there. There isn't an electrostatic or magnetic force, right? So, there is nothing pushing on the car towards the wall. However, if there was only the force from the wall pushing to the right, wouldn't the car accelerate to the right? Yes. It does.
Remember that acceleration is a change in velocity. If a car is moving in a circle at a constant speed, the velocity is changing since the direction of motion of the car is changing. This is called centripetal acceleration. The magnitude of this acceleration is:
Remember, the direction of this acceleration is towards the center of the circle. It has to be since the force is in that direction.
Minimum Friction
Let me use this centripetal acceleration to determine the minimum coefficient of static friction for this car to stay on the wall. I already have the force diagram above. From this I can say that the net vertical force (I will call this the y-direction) is zero since it doesn't accelerate in this direction. For the x-direction, the net force is not zero. This would mean:
Now, for the frictional model I will use this: