Calculating the work against gravity?

In summary, the conversation is about calculating the work required to build a tower out of bricks with a given height and base. The density of the bricks is 80 lb/ft^3 and the acceleration of gravity is assumed to be 32 ft/s^2. The process involves finding the volume and mass of each layer, then taking the integral to calculate the total force. The final answer should be 1.6x10^6 ft-lb, but there is confusion about the units and the given solution manual.
  • #1
mscott
4
0
Calculate the work against gravity require to build the structure out of brick. Assume the brick has a density of 80 lb/ft^3.

A tower has a height of 20ft and a square base of side 10ft.

This is what I tired to do. I may have gotten it right, but the units or something may have been off. I am hoping one of you will be able to help me.

Volume of layer = 10 x 10 Δy ft^3 = 100Δy ft^3
Mass of layer = 80 lb/ft^3 x 100Δy ft^3
Force on layer = 9.8 x 80 x 100Δy = 78400

Taking the integral of 78400y from limits 0 to 20 equals 15,680,000, but the answer in my solutions manual says the answer should be 1.6x10^6 ft-lb.

Can anyone help me out?
 
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  • #2
What is the acceleration of gravity in ft/s2?
 
  • #3
I'm not sure. Those were the only givens.
 
  • #4
I guess you are supposed to know that g = 32 ft/s2. Use that.
 

1. How do you calculate the work against gravity?

The work against gravity is calculated by multiplying the force of gravity (typically in Newtons) by the vertical displacement (typically in meters).

2. What is the formula for calculating work against gravity?

The formula for calculating work against gravity is W = F × d, where W is the work, F is the force of gravity, and d is the vertical displacement.

3. What unit is used to measure work against gravity?

The unit used to measure work against gravity is the Joule (J), which is equivalent to 1 Newton-meter (N∙m).

4. How does the angle of elevation affect the work against gravity?

The angle of elevation does not affect the work against gravity as long as the vertical displacement remains the same. However, if the angle changes, the displacement and work may also change.

5. What other factors can affect the calculation of work against gravity?

Other factors that can affect the calculation of work against gravity include the mass of the object, the acceleration due to gravity, and any external forces acting on the object.

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