A 73-ton monolith is transported on a causeway that is 2500 feet long and has a slope of about 2.2°. How much force parallel to the incline would be required to hold the monolith on this causeway?
assuming no friction, consider the cases of
0°: 0 force
90°: full weight
Looks like weight * sin(angle)
To calculate the force required to hold the monolith on the causeway, we first need to find the component of gravity that acts parallel to the incline. We can use the formula:
Force (parallel) = Weight × sin(θ)
where:
Weight = mass × gravity
θ = angle of the incline
Given:
Weight of the monolith = 73 tons
Length of the causeway = 2500 feet
Slope of the incline = 2.2°
First, let's convert the weight from tons to pounds:
Weight = 73 tons × 2000 pounds/ton
Weight = 146,000 pounds
Next, let's convert the slope from degrees to radians:
θ = 2.2° × π/180
θ ≈ 0.0383 radians
Now we can calculate the force parallel to the incline:
Force (parallel) = 146,000 pounds × sin(0.0383)
Force (parallel) ≈ 146,000 pounds × 0.0381
Force (parallel) ≈ 5566.6 pounds
Therefore, approximately 5566.6 pounds of force parallel to the incline would be required to hold the monolith on this causeway.
To find out the force required to hold the monolith on the causeway, we need to consider the gravitational force acting on the monolith and break it down into components.
First, let's calculate the component of the weight parallel to the incline using the formula:
Force parallel = Weight * sin(θ)
Where:
Weight = mass * gravity
θ = angle of the incline
Given that the monolith weighs 73 tons, we first convert it to pounds:
Weight = 73 tons * 2000 lbs/ton (Since 1 ton = 2000 lbs)
Weight = 146,000 lbs
The angle of the incline is given as 2.2°, but it needs to be converted to radians for the trigonometric function (sin) to work:
θ (in radians) = 2.2° * π/180°
Now, we can calculate the force parallel:
Force parallel = 146,000 lbs * sin(2.2° * π/180°)
Calculating this value, we find that the force parallel required to hold the monolith on the causeway is approximately 561.45 lbs.