Question

Your cat is begging to leave your room so, in frustration, you throw a 20 cm long knife with a mass of 250 g at your door which has a mass of 10 kg and is 0.7 m wide. The door is free to rotate about a vertical axis through its hinges. You observe that the knife is perfectly balanced (ie. the centre of mass of the knife is exactly at its centre) and is rotating at a speed of 6 rev/s just before striking the door.

1. What is the (linear) velocity of the knife just before it strikes the door?
2. If the knife becomes perpendicularly embedded in the centre of the door, find the angular speed of the door as it swings open.
3. How long does it take the door to swing far enough that the cat can leave your room? Your cat is only slightly overweight but still requires a 20 cm wide opening to escape.
4. Find the change in kinetic energy. Is energy conserved?

Answer 1

Sol:

Here length of knife is 20 cm hence radius of rotation r = 10 cm
Angular speed

Hence linear velocity of knife ia given as-

Now the linear speed of the center of mass of the door is given as-

Hence angular velocity of door is-

Now linear speed of edge of the door is

Now time taken to get 20 cm opening is-