Understanding Hooke's Law and Springs

The video tutorial covers Hooke's Law, explaining the relationship between force, displacement, and the spring constant. It includes example problems to calculate the spring constant, determine the force required to stretch a spring, and analyze work and elastic potential energy. The tutorial also discusses the concepts of positive and negative work in the context of spring mechanics.

What is the relationship between the force applied to a spring and its displacement according to Hooke's Law?

• Force is equal to the square of displacement.

• Force is directly proportional to displacement.

• Force is independent of displacement.

• Force is inversely proportional to displacement.

If a spring constant is 50 N/m, how much force is needed to stretch the spring by 2 meters?

• 100 N

• 50 N

• 200 N

• 25 N

Which spring is stiffer: one with a spring constant of 300 N/m or one with 50 N/m?

• The spring with 50 N/m

• The spring with 300 N/m

• Stiffness is not related to the spring constant

• Both are equally stiff

How do you convert 45 centimeters to meters?

• Multiply by 100

• Divide by 100

• Add 100

• Subtract 100

What is the spring constant if a force of 250 N stretches a spring by 0.24 meters?

• 1041.6 N/m

• 600 N/m

• 250 N/m

• 0.24 N/m

What is the formula for work done by a variable force in stretching a spring?

• Work = Force x Displacement

• Work = Displacement / Force

• Work = 1/2 x Force x Displacement

• Work = Force / Displacement

How is the work done by a spring related to the area under the force-displacement graph?

• It is unrelated to the area under the curve.

• It is half the area under the curve.

• It is twice the area under the curve.

• It is equal to the area under the curve.

What is the formula for elastic potential energy stored in a spring?

• kx^2

• kx

• 1/2 kx^2

• 1/2 kx

If a spring with a constant of 1800 N/m is stretched by 0.25 meters, what is the elastic potential energy stored?

• 56.25 J

• 450 J

• 0.25 J

• 1800 J

What happens to the work done by a spring when the force and displacement vectors are in opposite directions?

• The work is doubled.

• The work is positive.

• The work is zero.

• The work is negative.