Worksheet Introduction to Springs
You may use g = 10 m/sec2 in these exercises.

 The spring in a scale in the produce department of a supermarket stretches 2.5 cm when some bananas weighing 10 newtons are placed on the scale. The spring constant for this spring is

 When a 1.50-kg mass is placed on a spring with a spring constant of 30.0 newtons per meter, the spring is stretched 0.490 meter. How much energy is stored in the spring?

 A 5-N force causes a spring to stretch 0.2 meter. What is the potential energy stored in the stretched spring?

Refer to the following information for the next two questions.

In each of the following systems every spring has a spring constant of 50 N/m.
Which of the following systems has the smallest spring constant?
 What is the spring constant for the next system?

Refer to the following information for the next five questions.

A spring is compressed between two objects with unequal masses, m and M, held together by a string as shown below. The objects are initially at rest on a horizontal frictionless surface. The string is then cut.

As they are forced apart by the release of a compressed spring, which of the following quantities will have the same magnitude for both blocks?
Which statement(s) is(are) true?

 Suppose the small block has a mass of 1.2 kg and the large block has a mass of 1.8 kg and the 1.8-kilogram block moves to the right at 2.0 meters per second when the compressed spring is released. What is the speed of the 1.2-kilogram block after the spring is released?

 What is the total kinetic energy of the two blocks after the spring is released?

 If the spring was originally compressed 10 cm before the string was cut, what was its elasticity constant?

Refer to the following information for the next two questions.

A block of mass M is initially at rest on a frictionless floor, as shown in the accompanying figure. The block, attached to a massless spring with spring constant k, is initially at its equilibrium position. An bullet with mass m and velocity v is shot into the block The bullet embeds in the block.

 What is the speed of the bullet-block combination immediately after the collision before the spring begins compressing?

What will be the maximum compression of the spring?
Refer to the following information for the next question.

A mass m, attached to a horizontal massless spring with spring constant k, is set into oscillation by first compressing it a distance A from its equilibrium position and then releasing it.
What is the speed of the mass when it passes through its equilibrium position?
Refer to the following information for the next question.

A projectile of mass m is fired horizontally from a spring gun that rests on a horizontal frictionless surface. The mass of the gun is M.

If the kinetic energy of the projectile after firing is E, the gun will recoil with a kinetic energy equal to: