A small coin, initially at rest, begins falling. If the clock starts when the coin begins to fall, what is the magnitude of the coin\'s displacement between t1 = 0.300 s and t2 = 0.499 s?
To find the magnitude of the coin's displacement between t1 = 0.300s and t2 = 0.499s, we need to calculate the distance the coin has fallen in this time interval.
The equation for the distance fallen by an object in free fall is given by:
d = (1/2)gt^2
Where:
d = distance fallen
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Let's calculate the distance fallen at t1 = 0.300s:
d1 = (1/2)gt1^2
= (1/2)(9.8 m/s^2)(0.300s)^2
Now, let's calculate the distance fallen at t2 = 0.499s:
d2 = (1/2)gt2^2
= (1/2)(9.8 m/s^2)(0.499s)^2
To find the magnitude of the coin's displacement between t1 and t2, we subtract the distance fallen at t1 from the distance fallen at t2:
Magnitude of displacement = d2 - d1
Now, let's substitute the values and calculate the magnitude of the coin's displacement between t1 = 0.300s and t2 = 0.499s.
To find the displacement of the coin between t1 = 0.300 s and t2 = 0.499 s, we can use the equations of motion for constant acceleration:
displacement = initial velocity * time + (1/2) * acceleration * time^2
In this case, since the coin is initially at rest, the initial velocity (u) is equal to zero. We also need to know the acceleration (a) of the coin during its fall.
To determine the acceleration, we need to consider the force acting on the coin. The only significant force acting on the coin during free fall is the force due to gravity. Using Newton's second law of motion (F = m * a) and knowing that the weight (w) of the coin is equal to the force due to gravity (w = m * g, where g is the acceleration due to gravity), we can determine the acceleration.
a = w/m
The weight of an object can be calculated using its mass (m) multiplied by the acceleration due to gravity (g). On Earth, the acceleration due to gravity is approximately 9.8 m/s^2.
Now, let's calculate the weight of the coin using its mass and the acceleration due to gravity:
weight = mass * acceleration due to gravity
Given that the mass of the coin is not provided, we cannot calculate the weight or acceleration accurately. Therefore, without additional information, we cannot determine the magnitude of the coin's displacement between t1 = 0.300 s and t2 = 0.499 s.