What is meant by the period of a pendulum?
1 answer:
Answer:
The time it takes for the pendulum to make one complete cycle
Explanation:
The period of a pendulum is the time it takes for the pendulum to make one complete oscillation, which means the time it takes for the pendulum to come back to its original position (so, one left swing+one right swing).
The period of a pendulum is given by the formula
where L is the length of the pendulum and g is the acceleration due to gravity. As we can see from the equation, the period of a pendulum does not depend on the mass attached to the pendulum, but only on its length and on the strength of the gravitational field.
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The key to solve this problem is the conservation of momentum. The momentum of an object is defined as the product between the mass and the velocity, and it's usually labelled with the letter :
The total momentum is the sum of the momentums. The initial situation is the following:
(it's not written explicitly, but I assume that the 5-kg object is still at the beginning).
So, at the beginning, the total momentum is
At the end, we have
(the mass obviously don't change, the new velocity of the 15-kg object is 1, and the velocity of the 5-kg object is unkown)
After the impact, the total momentum is
Since the momentum is preserved, the initial and final momentum must be the same. Set an equation between the initial and final momentum and solve it for , and you'll have the final velocity of the 5-kg object.