Find mass of load that falls off truck

In summary, a truck with a total mass of 7500 kg was climbing a 15 degree incline at a steady 15 m/s when its poorly secured load fell off. After losing the load, the truck began to accelerate at 1.5 m/s^2. Using the equations ΣF = Fg + n + F1 = ma, where n is the normal force and F1 is the parallel force, it was determined that the mass of the load was approximately 2785.48 kg.
  • #1
Andy Salter
17
1

Homework Statement


A truck with a heavy load has a total mass of 7500 kg. It is climbing a 15 degree incline at a steady 15 m/s when, unfortunately, the poorly secured load falls off! Immediately after losing the load, the truck begins to accelerate at 1.5 m/s 2 . What was the mass of the load? Ignore rolling friction.

Homework Equations


ΣF = Fg + n + F1 = ma , where n is the normal force and F1 is the parallel force

The Attempt at a Solution


Before the load falls off we know a = 0 therefore
ΣF = Fg + n + F1 = 0

Fg before fall = 9.81 m/s^2 * 7500 kg = 73575 N

Fgx before fall = -73575*Sin(15) = -19042

Because ΣFx = 0 before fall, Fgx = -F1x

=> F1x = 19042 N

After fall we have:

Fx = 19042 + Fgx = FgSin(15) = m*1.5
Fy = 0

I'm not sure where I need to go from here. I need to find m so I can find the difference, but I can't do this without either the magnitude of Fg or Fgx. Not sure how I can find these...
 
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  • #2
Welcome to PF!

Is there a way to express Fg in terms of m?
 
  • #3
Ok so I assume you mean Fg = ma = 9.18m

I guess this gives me these simultaneous equations:

Fg = 9.81m
Fg = 1.5m / Sin(15)

But the solution of this is Fg = m = 0, so there's something wrong o_O
 
  • #4
Andy Salter said:
Fg = 9.81m
OK

Fg = 1.5m / Sin(15)
How did you arrive at this?
 
  • #5
Fx = 19042 + Fgx = FgSin(15)
Fy = 0
=> FgSin(15) = Fx = F = ma = 1.5m
=> Fg = 1.5m/Sin(15)
 
  • #6
Andy Salter said:
Fx = 19042 + Fgx = FgSin(15)
The first equality looks good. But I don't understand the second equality. How did you get 19042 + Fgx = FgSin(15)?
 
  • #7
My understanding was that Fx = Fgx = FgSin(15)
 
  • #8
Oh, wait, I see why that is wrong haha
 
  • #9
Fx = 19042 + Fgx = 19042 + FgSin(15) = 1.5m

which gives the simultaneous equations:

Fg = 9.81m
Fg = (1.5m - 19042)/ Sin(15)

With solutions:

f = -46249 and m = 4714.52

Therefore:
Δm = 7500 - 4714.52 = 2785.48 kg

Yes?
 
  • #10
Andy Salter said:
Fx = 19042 + Fgx = 19042 + FgSin(15) = 1.5m
Does Fgx = +FgSin(15) or does Fgx = - FgSin(15)?
which gives the simultaneous equations:Fg = 9.81m
Fg = (1.5m - 19042)/ Sin(15)

With solutions:

f = -46249 and m = 4714.52

Therefore:
Δm = 7500 - 4714.52 = 2785.48 kg

Yes?
Basically this is correct except for sign errors stemming from the wrong sign for Fgx. I think your results for m and Δm are correct.
 
  • #11
Ah yes, you are indeed right. Thankyou for your help :)
 
  • #12
OK. Good work.

When solving the two equations

Fg = 9.81m
19042 - FgSin(15) = 1.5m

it might be easier to just substitute the expression for Fg from the first equation into the second equation. So, the second equation becomes

19042 - 9.81m Sin(15) = 1.5m

Then you can solve this for m. But your method of doing the algebra is OK.
 

1. How do you calculate the mass of a load that falls off a truck?

To calculate the mass of a load that falls off a truck, you will need to know the velocity and acceleration at which it fell, as well as the distance it fell. You can use the equation m = F/a to calculate the mass, where F is the force of gravity and a is the acceleration due to gravity (9.8 m/s²).

2. Why is it important to find the mass of a load that falls off a truck?

Knowing the mass of a load that falls off a truck is important for a few reasons. Firstly, it allows for accurate record keeping and tracking of the truck's cargo. It also helps determine the cause of the accident and can be used for insurance purposes. Additionally, knowing the mass can help with proper disposal and cleanup of any spilled materials.

3. What factors can affect the mass of a load that falls off a truck?

Several factors can affect the mass of a load that falls off a truck. These include the material of the load, the speed and acceleration of the truck, and any external forces such as wind or bumps on the road. The angle of the truck's bed or trailer can also affect the mass as it can impact the force of gravity acting on the load.

4. Can the mass of a load that falls off a truck vary during transportation?

Yes, the mass of a load that falls off a truck can vary during transportation. This can occur due to shifting of the load, changes in temperature, or evaporation of liquids. It is important to regularly check the mass of the load during transportation to ensure that it is within the proper weight limit and to prevent any accidents.

5. Are there any safety precautions to take when finding the mass of a load that falls off a truck?

Yes, there are several safety precautions to take when finding the mass of a load that falls off a truck. Firstly, make sure to wear appropriate protective gear such as gloves and safety glasses. It is also important to secure the area and make sure there are no other potential hazards. Additionally, be cautious when handling any spilled materials, especially if they are hazardous. If possible, it is best to have a trained professional handle the cleanup process.

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