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In this lesson, we will learn how to use F = kx (Hooke's Law) and E = ½kx² to find the force and the potential energy of a compressed spring.

Q1:

In the movie Monty Python and the Holy Grail, a cow of mass 110 kg is catapulted from the top of a castle wall 9.1 m high, onto the people down below. The cow is launched from a spring of with a constant of 1 . 1 × 1 0 4 N/m that was initially compressed by 0.50 m from equilibrium. The gravitational potential energy is set to zero at the base of the castle wall.

What is the gravitational potential energy of the cow as it just clears the castle wall, treating the cow as a point particle?

What is the elastic spring energy of the cow before the catapult is released?

What is the speed of the cow at the instant that it hits the ground?

Q2:

A box that has 50 J of kinetic energy slides on a frictionless surface. The box hits a spring and compresses the spring a distance of 25 cm from its equilibrium length. If the same box with the same initial energy slides on a rough surface, it only compresses the spring a distance of 15 cm. How much energy must have been lost by the box when sliding on the rough surface?

Q3:

The spring of a spring gun has a force constant 𝑘 = 1 2 / N c m . When the gun is aimed vertically upward, a 15-g projectile is shot to a height of 5.0 m above the end of the expanded spring, as shown in the accompanying diagram. How much was the spring compressed initially?

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