Stretching a spring analysis and calculations (F=ke) | Exit Quiz | Oak National Academy

Two variables are directly proportional. Which of the following statements about the two variables are correct?

• When one variable doubles, the other variable doubles.

• When one variable increases by 10, the other variable increases by 10.

• When one variable becomes 5 times greater, the other becomes 5 times greater.

• When one variable halves, the other variable halves.

Answer explanation

When one variable is multiplied (or divided) by a number, the other variable is multiplied (or divided) by the same number. However, when one variable increases by an amount, the other does not necessarily increase by the same amount.

The following graphs show extension against applied force for three different springs. The scales are the same on all of the graphs. Which graph represents the spring with the lowest spring constant?

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Answer explanation

The spring with the steepest graph of extension against force has the lowest spring constant. This spring requires the least force to produce a particular extension. It also has the greatest extension for a particular force.

For elastic deformation, extension (or compression) is directly proportional to the force applied. What is the name of this law, and how is it expressed as an equation?

• Hooke’s law

• Newton’s law

Cars have stiff suspension springs to ensure a smoother ride. If the spring constant of one of these springs is 60 000 N/m, the force needed to compress the spring by 2.0 cm is ___ N.

Answer explanation

There are 100 centimetres in a metre, so 2.0 cm = 0.020 m. Force = spring constant × extension = 60 000 × 0.020 = 1200 N.

A spring has an unstretched length of 0.6 m. When a force of 200 N is applied, it stretches to a length of 1.0 m. What is the spring constant of the spring?

• 0.002 N/m

• 0.005 N/m

• 200 N/m

• 500 N/m

Answer explanation

Extension = stretched length – unstretched length = 1.0 – 0.6 = 0.4 m. Spring constant = force ÷ extension = 200 ÷ 0.4 = 500 N/m.

Springs P and Q are the same length. The spring constant is 5000 N/m for P and 10 000 N/m for Q. Equal forces stretch P and Q elastically. The extension of P is 8 cm. What is the extension of Q?

• 4 cm

• 8 cm

• 16 cm

• 64 cm