Explore BrainMass

the acceleration of the ladder extension on the firetruck

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

The firetruck us moving forward at a speed of 35 MPH and is decelerating at a rate of 10ft/sec.^2. Simultaneously, the ladder is being raised and extended.
At the instant considered the angle Ø is 30° and is increasing at a rate of 10 degrees/sec . Also at this instant the extension b of the ladder is 5 ft and Vb = 2 feet / sec and ab = -1 ft/sec^2. Where Vb is the rate of extension of part b in ft/sec and ab is the acceleration of the extension of part b in ft/sec^2.

Find the acceleration of point A with

1. Respect to the truck
2. Respect to the ground

SOLUTION This solution is FREE courtesy of BrainMass!

The fire truck us moving forward at a speed of 35 MPH and is decelerating at a rate of 10ft/sec.^2. Simultaneously, the ladder is being raised and extended.
At the instant considered the angle Ø is 30° and is increasing at a rate of 10 degrees/sec . Also at this instant the extension b of the ladder is 5 ft and Vb = 2 feet / sec and ab = -1 ft/sec^2. Where Vb is the rate of extension of part b in ft/sec and ab is the acceleration of the extension of part b in ft/sec^2.

Find the acceleration of point A with

1. Respect to the truck
2. Respect to the ground

Let's define the xyz coordinates as shown in the following figure

B is the point on the truck. For the truck, its velocity and acceleration is to the right:

Then we need to decompose them to the current coordinates:

For the extension part b:

The velocity is

The acceleration is

The angular velocity is counterclockwise and perpendicular to the xy-plane:

The angular acceleration is 0 since angular velocity is constant.

Using the equation to calculate the acceleration of point A with respect to ground:

In the above equation:

And

Therefore, the acceleration of point A with respect to the ground is

The acceleration of point A with respect to the truck is

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!