# Springs

## Mechanical Aptitude Test - Springs

A Spring is a piece of metal that can be extended or compressed by an external force which then returns to it's original lenght when that force is no longer applies.

There are many different types of spring including, spiral coil, leaf springs and torsion springs. Springs are used in many applications including clocks, vehicle suspensions etc. In the type of questions that you will be asked in mechanical aptitude tests, you can assume that springs behave in a linear way. That is, doubling the force applied will stretch or compress the spring twice as much.

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**Springs**

Definition

#### Below you will find some mechanical aptitude test spring questions and answers:

##### Springs - Example 1

The figure shows a mass of 5 kg attached to a rope and a spring, we know that the tension in the rope is 10 N, the spring must be:

A) Extended

B) Compressed

C) Neutral

Answer: B

The weight of the mass is about 50 N, so a force must be acting upwards to support the weight a little bit because the tension in the rope is less than the weight, which means the spring must be compressed.

##### Springs - Example 2

What is the force needed to move the mass 2 inches to the right as shown in this figure? Neglect friction.

A) 24 pounds

B) 34 pounds

C) 10 pounds

Answer: A

The force of the spring is equal to the constant of the spring times the displacement, which equals to 12 * 2 = 24 pounds

##### Springs - Example 3

By putting the 2 kg mass first, the spring displaces a distance of 5 mm, then we replace that spring with another one and add another 3 kg mass, we see that it displaces the same distance, the second spring is:

A) Double the first spring's stiffness

B) More than double

C) less than double

Answer: C

The second spring endured 1.5 times the weight with the same displacement, so it's 1.5 times as stiff as the first.

##### Springs - Example 4

The 3 kg collar is released from rest at height (h) from the spring, we see that it deforms a distance (s) on impact, we then replace the spring and do the experiment again, this time, to see the new spring deform a distance (2s), which of the springs is stiffer ?

A) The first spring.

B) The second spring

C) Stiffness doesn't depend on deformation only.

Answer: A

The potential energy consumed by the spring is equal to 0.5 * stiffness * displacement2

As the first spring deformed slightly less, it must have higher stiffness to consume the same amount of energy from the mass.

##### Springs - Example 5

Which configuration do you think has more overall stiffness?

A) The right one.

B) The left one.

C) Both have the same stiffness.

Answer: B

Suppose we displace each mass to the left a distance (s), now on the left figure, each spring will deform a distance (s) hence, will act by a force (k*s), so a total force of (2ks).

Now the right figure, each spring will deform with (0.5 * s) and will act with a force of (0.5ks) and only one spring is attached to the mass, so a total force of (0.5ks).

Because the left system has more force for the same displacement, it has more stiffness.