Can anyone help me with my physics homework?

Question

In mountainous regions, road builders construct runaway truck ramps near the bottoms of long hills. These ramps allow a truck with failed (not working) brakes to leave the main road and coast uphill to a stop on sand or gravel-filled paths. Explain why the sand or gravel helps stop the truck. (Hint: Think about running on a very sandy beach.)

Answer 1

From a physics perspective, how would you model the stopping of the truck?

First, the truck has a very large mass, and is likely moving a high velocity since the brakes have failed.

The ramp is sloped upward, so the gain in potential energy will help stop the truck, but it only works as m*g*h
sine the truck enters the ramp with kinetic energy of:
1/2*m*v^2
a smooth ramp would require vertical gain of:
h= 1/g* 1/2* v^2

also keep in mind that it is sloped
so the h=L*sin(a)
where a is the angle up. Obviously the slope has to be such that the truck will safely transition from the downward motion and up the ramp.

Now consider a frictional force that helps stop the truck, The higher the coefficient of friction, the more powerful the force.

Sand or gravel is loose, so the truck tires sink into the material. Again, we want to keep the driver from being thrown through the windshield, or the axles being torn from the chassis of the truck, so the amount of force must be controlled.

With a coefficient of friction of u, the force of friction is
m*g*u*cos(a)

if we want the stopping force to be less than twice the force of gravity, then 2*m*g=m*g*u*cos(a)+m*g*sin(a)
the two variables are the angle a, and the coefficient of friction u.
An engineer would optimize the two so that the truck and the driver survive, and the ramp is inexpensive to build and maintain.

j

Answer 2

To answer this - as your teacher pointed out, you must think of sand. When you walk/run on sand the reason that running on it is so hard is that every time you attempt to push off it, it gives way, requiring runners to exert approximately 1.6 times the energy that would be required to maintain the same speed on solid ground. For walkers, make that 2.1 to 2.7 times for energy.

Lets now work this into the truck scenario. The weight of the truck and the traction that the truck would like to produce is slowed down because the sand or gravel has lots of dead space. When the weight of the truck is exerted on the sand or gravel, the particular matter is compressed which now requires the truck more energy to move forward. In other words, most of the kinetic energy that the truck has, is now transferred to the compression of the sand.

Answer 3

The wheels of the truck can't make traction in the sand. Can't get a good enough grip in the sand.

Answer 4

Sand creates friction. It'll slow anything down.