What is the momentum of a 3 kg cat sitting on a windowsill at a height of 15 meters? - briefly
The momentum of an object is defined as the product of its mass and velocity. Since the cat is sitting stationary on a windowsill, its velocity is zero. Therefore, the momentum of the 3 kg cat is zero.
What is the momentum of a 3 kg cat sitting on a windowsill at a height of 15 meters? - in detail
Momentum is a fundamental concept in physics, defined as the product of an object's mass and its velocity. In the scenario described, we have a 3 kg cat sitting on a windowsill at a height of 15 meters. To determine the momentum, we need to consider the cat's mass and its velocity. At the moment the cat is stationary on the windowsill, its velocity is zero.
The formula for momentum (p) is given by:
p = m * v
where:
- m is the mass of the object (in this case, the cat),
- v is the velocity of the object.
Given that the cat's mass (m) is 3 kg and its velocity (v) is 0 m/s (since it is sitting still), we can substitute these values into the formula:
p = 3 kg * 0 m/s = 0 kg·m/s
Therefore, the momentum of the 3 kg cat sitting on the windowsill is zero. This is because momentum requires motion, and a stationary object has no momentum. However, if the cat were to jump off the windowsill, its velocity would change, and thus its momentum would also change. The momentum would then depend on the cat's velocity at any given moment during its descent or subsequent motion.
To further illustrate, if the cat were to fall freely from the windowsill, its velocity would increase due to the acceleration caused by gravity. The velocity (v) of a freely falling object can be calculated using the formula:
v = √(2gh)
where:
- g is the acceleration due to gravity (approximately 9.81 m/s²),
- h is the height from which the object falls (in this case, 15 meters).
Substituting the values, we get:
v = √(2 9.81 m/s² 15 m) ≈ 17.15 m/s
This velocity would be achieved just before the cat hits the ground, assuming no air resistance. At this point, the momentum of the cat would be:
p = 3 kg * 17.15 m/s ≈ 51.45 kg·m/s
This example highlights how momentum changes with the velocity of the object. In the initial scenario, the cat's momentum is zero due to its lack of motion. However, once the cat starts moving, its momentum becomes a crucial factor in understanding its dynamics.