Will the Truck Roll Back Down the Slope Due to Insufficient Friction?

[tobes_oz]

Homework Statement

PROBLEM 4 (15 marks)
Using the information in problem 3 and the static coefficient of friction of the road as 0.7, will the truck be in danger of rolling back down the slope? Use appropriate diagrams and include all your working to justify your answer.
PROBLEM 3 (15 marks)
Roads going down through mountains regions are often steep. As a precaution for heavy traffic areas, particularly for trucks, safety ramps are constructed in case vehicles’ brakes fail.
A truck’s brakes have failed while traveling down the Toowoomba Range. The truck gains velocity as it has traveled the range, before the driver finds the safety ramp. The truck’s velocity has increased to 100km/h by the time it has reached the start of the safety ramp, the ramp has a slope of 30° from the horizontal and the truck takes 10s to roll to a complete stop. For a minimum safe stopping distance, what will be the total horizontal distance of the escape ramp?

Homework Equations

I've done question 3, I think it was fairly easy. The horizontal leg of the ramp is 120m, the incline leg is 139m. Rate of acceleration (deceleration) is -2.78m/s/s

question 4, I am completely stumped. I have drawn a free box diagram and indicated all of the relevant forces, but I have no idea how to calculate what's necessary to find a solution?

The Attempt at a Solution

Don't know where to start!

 

[cupcuppycup]

look at the two forces acting on the truck. the force of friction and the force of the truck moving. each force is going an opposite way so depending on which force is greater, the truck will move in that direction. it doesn't give mass so i don't think mass will matter because F=ma and Force of Friction=UFn

 

[tobes_oz]

thanks for the reply.

the truck isn't moving though in this particular question. It is assuming the truck has already rolled up the ramp and come to a stop. The question is asking whether the truck will roll back down the ramp, the only figures given are the static co-efficient of friction and the angle of the ramp. I cannot for the life of me work out how to come to a solution without having mass of the truck given

 

[Doc Al]

Call the mass of the truck 'm' and keep going. (You'll discover that you won't need the actual value of the truck's mass to answer the question.)

 

[rwisz]

As a scientist, it is important to approach problems like this using a logical and systematic approach. Let's break down the problem and use the information given to find a solution.

First, we need to determine the forces acting on the truck as it travels down the slope. The main forces at play here are gravity and friction. Gravity is pulling the truck down the slope, while friction acts in the opposite direction, trying to slow down the truck's movement.

Next, we need to consider the static coefficient of friction of the road, which is given as 0.7. This means that the maximum friction force that can act on the truck is 0.7 times the normal force (the force exerted by the road on the truck). We can calculate the normal force by using the weight of the truck, which is given as a mass of 10,000 kg, and the acceleration due to gravity (9.8 m/s^2).

Now, we can use the information from problem 3 to calculate the velocity and acceleration of the truck. We know that the truck's velocity is 100 km/h, which is equivalent to 27.78 m/s. We also know that the truck takes 10 seconds to come to a complete stop, which means that its average acceleration is -2.78 m/s^2.

Using Newton's second law of motion, F=ma, we can calculate the net force acting on the truck. We know that the net force is equal to the sum of the forces acting on the truck, which in this case are gravity and friction. So, we can set up the following equation:

Fnet = Fgravity + Ffriction

We can calculate Fgravity using the formula F=mg, where m is the mass of the truck and g is the acceleration due to gravity. We can then calculate Ffriction by multiplying the normal force by the coefficient of friction (Ffriction = μN).

Now, we need to determine if the net force is enough to overcome the truck's inertia and keep it from rolling back down the slope. We can do this by calculating the truck's acceleration using the formula a=Fnet/m. If the acceleration is negative, then the net force is not enough to stop the truck and it will roll back down the slope.

Finally, we can use the acceleration and the time it takes for the truck to come to a complete stop to calculate the distance traveled using the formula d=vt+