physics: obnoxious brat assigns his 0.0197-kilogram pet mouse Mickey the role of

Question

physics:

obnoxious brat assigns his 0.0197-kilogram pet mouse Mickey the role of stunt mouse by stuffing him into a spring gun and shooting him up into the air at some angle. The gun's spring has a force constant of 88.7 N/m and is initially compressed 0.121 m. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.23 m/s. How high above his initial location in the gun does Mickey soar? (In case you are worried, a miniature parachute opens at this point and Mickey lands safely. The brat is slightly less obnoxious than we thought.) Take g = 9.81 m/s2.

Explanation / Answer

Considering (mouse + spring) as a system

Initially the mouse is at rest and the spring is compressed, so the total energy of the system = Elastic potential energy of the spring = 0.5*spring_constant * square of compression = 0.5*88.7*(0.121)^2 = 0.6493 Joules

At a height H above its initial position, the mouse has a horizontal speed of 2.23 m/s

So, kinetic energy of mouse at this point = 0.5*m*v^2 = 0.5 * 0.0197 * 2.23^2 = 0.048983 Joules

The spring is now relaxed so its final elastic potential energy is zero

Therefore, loss in energy of the system = (0.6493 - 0.048983) Joules = 0.6003 Joules

According to the law of conservation of energy, this loss in energy should be compensated by the gain in gravitational potential energy of the mouse.

Gravitational P.E. of mouse at height H = mgH = 0.0197*9.81*H = 0.1933* H Joules

Thus, 0.1933*H = 0.6003, H = 3.1062 m

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.