The Physics
Hypertextbook
Opus in profectus

# Springs

## Problems

### practice

1. Write something.
2. Write something else.
3. Write something different.
4. Write something completely different.

### numerical

1. A spring with a natural height of 57 mm is compressed by a 300 g mass to a new height of 51 mm.
1. Find the spring constant in SI units.
2. Find the length of the spring if the 300 g mass were replaced by a 400 g mass.
2. The graph on the right shows the applied force vs. the extension for a particular spring.
1. Find the spring constant.
2. Find the work done on the spring.
3. Find the potential energy stored in the spring.
3. A spring operated dart gun fires 10 g darts. Arming the gun requires 185 N of force and results in the shortening of the spring by 10 cm.
1. Find the spring constant.
2. Find the energy stored in the spring.
3. Find the muzzle velocity of the dart.
4. If the dart is launched vertically, how high will it rise? (Do not use an equation of motion to solve this problem. Use conservation of energy.)
4. The dart gun in the previous problem is fired horizontally at a 500 g squirrel. Find the speed of the squirrel after it was struck by the dart.
5. A 68 kg acrobat stands on a spring loaded platform as a part of a stunt. If the spring under the platform has a spring constant of 1.6 × 103 N/m, how far should the spring be compressed to vault the acrobat to a height of 5.0 m?
6. Estimate the elastic potential energy stored in the pole used in the pole vault given that elite vaulters are capable of heights in excess of 6 m and that world class sprinters can cover 100 m in about 10 s. (Assume that a typical male vaulter has a mass of about 80 kg.)

### algebraic

1. A block of mass m rests on a rough horizontal surface whose coefficient of kinetic friction is μk. The block is held in contact with one end of a spring which is compressed a distance x. The spring has a spring constant of k. The other end of the spring is fixed. If the block is released, over what distance will it travel from its initial position before it comes to rest? Express your answer in terms of the quantities provided in the description above (mμkxk) and the acceleration due to gravity (g).