Engineering Dynamics Problem

[rdg29]

1. Problem statement:

A 5000-lb truck is being used to lift a 1000-lb boulder B that is on a 200-lb pallet. Knowing the acceleration of the truck is 1 ft/s^2, determine the horizontal force between the tires and ground. The truck is on a horizontal plane with the boulder and pallet connected to a single pulley system off a cliff face.

Homework Equations

:[/B]

∑F = ma

3. Attempt at the solution:

[STRIKE]Assuming no friction.
[/STRIKE]
First, I separated the truck and the boulder with two separate FBD/Kinematic diagrams.

For the truck, I had 4 total forces acting on the body.

F = ? (horizontal force between the truck and the ground)
T = ? (tension in the cable)
N = 5000 lb
W = -5000 lb

Setting up the sum of the forces on the truck, we get:
∑F_y = 0
∑F_x = F - T
(ma)_sum = F - T

m_truck = 5000/32.2 = 155.280

Subbing in the known values:
155.280*1 ft/s^2 = F - T

Now, I moved to the pulley system:

The FBD consisted of 3 forces:

T = ? (tension in the cable)
W_b = Weight of the Boulder = 1000 lb
W_p = Weight of the Pallet = 200 lb

Setting up the sum of the forces, we get:

∑F_x = 0
∑F_y = T - W_b - W_p

Subbing in the known values:
m_{boulder+pallet} = (1000 lb + 200 lb)/32.2 = 37.267

(m_{boulder+pallet}*1 ft/s^2) = T - 1000-lb - 200-lb
T = 1237.267-lb

Use T to find F in the equation for the truck:
155.280 = F - 1237.267
F = 1392.5-lb

The problem I am running into however, is this does not match the answer I'm told to find. I'm wondering if it is just something simple that I'm missing here, so any guidance would be appreciated.

 

[PhanthomJay]

Looks ok to me except you should found off the number. There is friction,though, between driving tires and road. Otherwise, the truck couldn't move.

 

[rdg29]

Thanks for looking it over, and pointing out the friction error on my part. The overall error may end up being an error in the solution provided maybe? The solution listed is 765-lb for the force between the ground and the truck.

 

[PhanthomJay]

Must be a book error .

 

[rezeew]

Hi there,

Thank you for providing a detailed attempt at solving this engineering dynamics problem. It seems like you have set up the equations correctly and have made good progress in solving for the horizontal force between the truck and the ground.

One thing that may be causing the discrepancy between your answer and the expected answer is the assumption of no friction. In real-world situations, there will always be some level of friction present, especially in a pulley system. This could potentially affect the calculations and lead to a slightly different answer.

I would also recommend checking your units throughout the problem to ensure that they are consistent. For example, in your final calculation, you have used pounds (lb) for the weight of the boulder and pallet, but used the unit foot per second squared (ft/s^2) for the acceleration. This could potentially lead to an incorrect answer.

Overall, your approach to solving the problem seems sound and I would suggest double-checking your calculations and taking into account any potential sources of error, such as friction. I hope this helps and good luck with your future engineering problems!