Calculation max load on a scissor jack lifting a car

[vpatel28]

Homework Statement

I have to determine the max load a scissor jack must support when lifting a 6000lb car. I know where the center of gravity is acting and the potential locations (distances from the center of gravity) the car will be jacked up. I know the max force is less than 6000 lb.

Homework Equations

The Attempt at a Solution

I tried taking the moments about one of the tires and setting them equal to zero to solve for the max force at each location, but I know I'm doing something wrong.

 

[tiny-tim]

Welcome to PF!

Hi vpatel28! Welcome to PF!

… I tried taking the moments about one of the tires and setting them equal to zero to solve for the max force at each location, but I know I'm doing something wrong.

That should work …

show us what you got!​

 

[vpatel28]

I've attached a diagram of the geometry of the car. The more I think about the problem, I feel like I need to know which two tires the car will lean on for each case. Inspection tells me that it will lean on the two side tires for both cases.

Do I want to take the moment about one of the tires that car is leaning on? If I do that I get the following:

Case 1 - Lean on Back wheels
(6000)(8 ft) + -F(10) = 0
F= 4800 lb

Case 2 - Lean on Side Wheels
(-6000)(3) + (F)(6) = 0
F = 3000 lb

I'd appreciate any help in directing me in the right direction

 

[tiny-tim]

I've attached a diagram of the geometry of the car.

erm … noooo!

Do I want to take the moment about one of the tires that car is leaning on? If I do that I get the following:

Case 1 - Lean on Back wheels
(6000)(8 ft) + -F(10) = 0
F= 4800 lb

Case 2 - Lean on Side Wheels
(-6000)(3) + (F)(6) = 0
F = 3000 lb

Difficult to be sure without seeing a diagram,

but that certainly looks ok! ​

 

[vpatel28]

Sorry about that. Here is the attachment with the diagram

 

[tiny-tim]

I've attached a diagram of the geometry of the car. The more I think about the problem, I feel like I need to know which two tires the car will lean on for each case. Inspection tells me that it will lean on the two side tires for both cases.

ok, from the diagram the wheels are 12 ft apart front-to-back, and 6 ft apart side-to-side.

The jack points are 2ft behind or in front of the nearest wheel.

The c.o.m. is 4ft behind the front wheels and 8ft in front of the back wheels.

Case 1 - Lean on Back wheels
(6000)(8 ft) + -F(10) = 0
F= 4800 lb

Case 2 - Lean on Side Wheels
(-6000)(3) + (F)(6) = 0
F = 3000 lb

Yes, those equations are fine, except that in case 1, if the c.o.m. is nearer the front, won't the car overbalance onto the side?

 

[vpatel28]

If the the car leans on the side wheels for both cases then isn't the max force the same in both cases?

 

[tiny-tim]

If the the car leans on the side wheels for both cases …

It doesn't … it leans on the front wheels for a back jacking point, and on the side wheels for a front jacking point …

can you prove that?