# Springs

## Problems

### practice

Chest expander mass

(kg)position

(cm)0 026.5 1 040.0 2 054.0 3 068.5 5 097.5 6 112.5 7 127.5 8 143.5 - A teacher presses down on a spring loaded pop-up toy until the suction cup part of it catches. The teacher's class waits in anticipation. Without warning the suction breaks and the toy does what it's supposed to do — it pops up. The teacher records the toy's mass, its height height before and after being compressed, and the maximum height it attains after popping up.
Pop-up toy mass

of toyuncompressed

heightcompressed

heightmaximum

height16 g

0.016 kg11cm

0.11 m7 cm

0.07 m92 cm

0.92 m- the gravitational potential energy of the toy at its highest point relative to the table top
- the kinetic energy of the toy as it left the table
- the speed of the toy as it left the table
- the elastic potential energy of the toy after it was compressed
- the spring constant of the spring inside the toy

- Write something different.
- Write something completely different.

### numerical

- A spring with a natural height of 57 mm is compressed by a 300 g mass to a new height of 51 mm.
- Find the spring constant in SI units.
- Find the height of the spring if the 300 g mass were replaced by a 400 g mass.

The graph on the right shows the applied force *vs*. the extension for a particular spring.- Find the spring constant.
- Find the work done on the spring.
- Find the potential energy stored in the spring.

- 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.
- Find the spring constant.
- Find the energy stored in the spring.
- Find the muzzle velocity of the dart.
- 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.)

- 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 × 10
^{3}N/m, how far should the spring be compressed to vault the acrobat to a height of 5.0 m? - 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

- A block of mass m rests on a rough horizontal surface whose coefficient of kinetic friction is μ
. The block is held in contact with one end of a spring which is compressed a distance_{k}*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 ℓ 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 (*m*, μ,_{k}*x*,*k*) and the acceleration due to gravity (*g*).