Distance traveled by a accelerating truck with steel load.

[blackkeys]

Distance traveled by an accelerating truck with a steel load. With a twist!

Homework Statement

Consider a large truck carrying a heavy load such as steel beams. A significant hazard for the driver is that the load may slide forward crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a 10,000kg load sits on the flat bed of a 20,000kg truck moving at 12.0m/s. Assume the load is not tied down to the truck and has a coefficient of static friction of 0.500 with the truck bed. Calculate the minimum stopping distance for which the load will not slide forward relative to the truck.

Homework Equations

Fsf is less then or equal to the coefficient of static friction * (mass * gravity)

A= (velocity final - velocity initial) / (total time)

change in x = original velocity in the x direction + acceleration in the x direction * time

The Attempt at a Solution

I know that both masses of the beams and truck are not relevant to the solution to the problem. However that's all I've been able to figure out. I think that if the truck is moving at 12m/s the bars must be resisting motion at 12m/s. Is this true? I wasn't sure which direction to go after determining that mass wasn't going to be any help. How could I use this to help solve the problem?

The solution to the problem is 14.7m

 

[PhanthomJay]

Homework Statement

Consider a large truck carrying a heavy load such as steel beams. A significant hazard for the driver is that the load may slide forward crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a 10,000kg load sits on the flat bed of a 20,000kg truck moving at 12.0m/s. Assume the load is not tied down to the truck and has a coefficient of static friction of 0.500 with the truck bed. Calculate the minimum stopping distance for which the load will not slide forward relative to the truck.

Homework Equations

Fsf is less then or equal to the coefficient of static friction * (mass * gravity)

A= (velocity final - velocity initial) / (total time)

change in x = original velocity in the x direction + acceleration in the x direction * time

The Attempt at a Solution

I know that both masses of the beams and truck are not relevant to the solution to the problem. However that's all I've been able to figure out. I think that if the truck is moving at 12m/s the bars must be resisting motion at 12m/s. Is this true? I wasn't sure which direction to go after determining that mass wasn't going to be any help. How could I use this to help solve the problem?

The solution to the problem is 14.7m

The acceleration of the beam load must be the same as the truck's acceleration in order for the load not to slide with respect to the truck. You'll need to calculate that acceleration of the load using Newton's 2nd law. The use your kinematic equations...you made in error in one of them for delta x.

 

[ogb p]

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I would first clarify the question and assumptions being made. Are we assuming that the truck is traveling on a flat surface, and that the load is evenly distributed on the truck bed? Are we assuming that the truck is accelerating at a constant rate, or is it already at a steady speed of 12 m/s? These details can affect the calculation of the minimum stopping distance.

Assuming that the truck is accelerating at a constant rate, we can use the equations provided to calculate the minimum stopping distance. The first step would be to calculate the acceleration of the truck using the given information. We can use the equation A= (velocity final - velocity initial) / (total time) and plug in the values, where velocity final is 0 m/s (since the truck is stopping), velocity initial is 12 m/s, and total time is unknown. This gives us an acceleration of -12 m/s^2.

Next, we can use the equation change in x = original velocity in the x direction + acceleration in the x direction * time to calculate the minimum stopping distance. Again, we plug in the values, where original velocity is 12 m/s, acceleration is -12 m/s^2, and time is unknown. This gives us a minimum stopping distance of 14.7 meters.

However, this calculation assumes that the load is not sliding at all during the stopping process. In reality, there will be some movement of the load due to the coefficient of static friction and the force of gravity. To address this, we could use a more complex model that takes into account the frictional force and the movement of the load.

Another approach would be to consider the maximum force of friction that the load can exert on the truck bed before sliding. We can use the equation Fsf is less then or equal to the coefficient of static friction * (mass * gravity) and plug in the values, where Fsf is the maximum force of friction, coefficient of static friction is 0.500, mass is 10,000 kg, and gravity is 9.8 m/s^2. This gives us a maximum force of friction of 49,000 N. We can then use this value to calculate the minimum stopping distance by setting it equal to the force of the truck's acceleration (mass of 20,000 kg * acceleration of -12 m/s^2). This gives us a minimum stopping distance of 16.3 meters.

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