Final answer:
To compress the spring 10 inches, we would need 10 times the force required to compress it 1 inch, totaling 500 pounds of force, based on Hooke's Law.
Step-by-step explanation:
To determine the amount of force needed to compress a spring 10 inches given that it compresses 1 inch for every 50 pounds of force, we can use Hooke's Law. Hooke's Law states that the force needed to compress or extend a spring is directly proportional to the displacement, which can be expressed as F = kx, where F is the force, k is the spring constant (force per unit displacement), and x is the displacement (compression or extension) of the spring.
In this case, we are given that 50 pounds of force compresses the spring by 1 inch. Therefore, for 10 inches of compression, we would need 10 times the force, because the relationship is linear. The calculation would be 50 pounds/inch * 10 inches, which gives us 500 pounds of force needed to compress the spring 10 inches.