a force of 1250 pounds compresses a spring 5 inches from its natural length. find the work done in compressing the spring 8 additional inches.
f=kd
1250=k5
k=250
then what do i do.
the answer choices are:
a.3250
b.21,125
c.18000
d.2000
e. none of these
Work = (1/2)* F * deflection
After 8 additional inches of deflection, the Force will increase to
(13/5)*1250 = 3250 lb
The total work done (from zero deflection) will be
(1/2)*3250 *13 = 21,125 in-lb
The original work done (for the first 5 inches of deflection) was
(1/2)*1250*5 = 3125 in-lb
The additional work done is
21,125 - 3125 = 18,000 in-lb
Another way to do this would be to calculate the spring constant k = 250 lb/in, as you have done. Then subtract
(1/2) k 5^2 from (1/2) k (13^2).
The difference is (1/2)*k * 144 = ?
work= force * distance, so you can set up an integral to solve for work
F=k*x, k=250
force =250x
distance =dx
so then you integrate(250x)dx from 0->(5+8)=21,125
idk if its right but its an answer choice
To find the work done in compressing the spring 8 additional inches, we can use the formula for work done on a spring:
Work = (1/2)k(deflection^2)
where k is the spring constant and deflection is the amount the spring is compressed.
In this case, we know that the force applied to compress the spring is 1250 pounds and it compresses 5 inches from its natural length. We also know that k = 250 pounds per inch.
Using the given information, we can calculate the work done for the first 5 inches of deflection:
Work = (1/2) * 250 * (5^2)
= (1/2) * 250 * 25
= 3125 inch-pounds
Now, we need to find the work done for the additional 8 inches of deflection:
First, we need to calculate the new force applied to compress the spring 8 inches:
New force = 1250 * (5+8)/5
= 1250 * 13/5
= 3250 pounds
Now, we can calculate the work done for the additional 8 inches of deflection:
Work = (1/2) * 250 * (13^2 - 5^2)
= (1/2) * 250 * (169 - 25)
= (1/2) * 250 * 144
= 18000 inch-pounds
Therefore, the work done in compressing the spring 8 additional inches is 18000 inch-pounds.
The correct answer choice is c. 18000.
To find the work done in compressing the spring 8 additional inches, you can use the formula:
Work = (1/2) * k * (deflection^2)
where k is the spring constant and deflection is the additional distance the spring is compressed.
From the given information, we know that the force of 1250 pounds compresses the spring by 5 inches. Thus, we can calculate the spring constant:
1250 = k * 5
k = 250 lb/inch
Now, we need to calculate the work done in compressing the spring by an additional 8 inches:
Work = (1/2) * k * (deflection^2)
= (1/2) * 250 * (8^2)
= (1/2) * 250 * 64
= 8000 lb * inch
Therefore, the work done in compressing the spring 8 additional inches is 8000 lb * inch.
However, the given answer options are in different units (e.g., 3250, 21,125, 18000, 2000). If you need to convert the units, please provide the necessary conversion factor or clarify the desired units for the answer.