A.) How much work must be done in order to compress a spring with an elastic constant of 400 lb / in and 1.75 inches?
*Note: 1.75" is the compression & 400#/in is k the constant.
B.)If 50 ft lbs of work is done on the same spring (in part a) in order to compress it, by how much is the spring shortened?
A.) To calculate the work done in compressing a spring, you can use the formula:
Work = (1/2) * k * x^2
where:
- Work is the amount of work done (in this case, we are looking for the work to be done)
- k is the elastic constant or spring constant (given as 400 lb/in)
- x is the displacement or compression of the spring (given as 1.75 inches)
Plugging in the values, we have:
Work = (1/2) * 400 lb/in * (1.75 in)^2
Calculating this, we get:
Work = 0.5 * 400 lb/in * 3.0625 in^2
Work = 612.5 lb * in
So, the amount of work required to compress the spring by 1.75 inches is 612.5 lb * in.
B.) To find out how much the spring is shortened when 50 ft lbs of work is done on it, we can rearrange the formula and solve for x:
x = √((2 * Work) / k)
where:
- x is the displacement or compression of the spring (what we are looking for)
- Work is the amount of work done on the spring (given as 50 ft lbs, which needs to be converted to lb * in)
- k is the elastic constant or spring constant (given as 400 lb/in)
First, let's convert 50 ft lbs to lb * in:
1 ft = 12 inches, so 50 ft = 50 * 12 inches = 600 inches
50 ft lbs = 600 inches * lb
Now we can plug in the values:
x = √((2 * 600 inches * lb) / 400 lb/in)
Calculating this, we get:
x = √(1200 inches^2 / 400 lb)
x = √3 inches
Therefore, when 50 ft lbs of work is done on the spring, it is shortened by √3 inches.