If the end of the ruler of length 1 m is raised by 25 cm, the wooden bar is sliding down at the constant speed. What is the acceleration of the bar if the height of the end is increased twice
To find the acceleration of the bar, we need to determine the change in velocity and the time it takes to reach that change.
First, let's calculate the change in height when the end of the ruler is raised by 25 cm. A meter is equal to 100 cm, so when the end of the ruler is raised by 25 cm, the change in height is 25 cm.
Next, if the height of the end is increased twice, the new change in height would be twice the previous change, which is 2 * 25 cm = 50 cm.
Now, to find the time it takes for the bar to slide down, we need to consider the motion as free fall. The distance traveled during free fall can be calculated using the equation:
s = ut + (1/2)gt^2
where s is the distance, u is the initial velocity, t is the time, and g is the acceleration due to gravity.
Since the bar is sliding down at a constant speed, its initial velocity, u, is zero. Therefore, the equation simplifies to:
s = (1/2)gt^2
We can plug in the new change in height, s = 50 cm = 0.5 m, into the equation:
0.5 = (1/2)g * t^2
Next, let's solve for the time, t:
1 = gt^2
t^2 = 1/g
t = √(1/g)
Finally, to find the acceleration, we need to calculate the change in velocity over time:
acceleration = change in velocity / time
The change in velocity is equal to the change in height, which is 50 cm or 0.5 m.
Plugging in the values, we have:
acceleration = 0.5 / √(1/g)
The acceleration of the bar can be calculated by using the acceleration due to gravity, which is approximately 9.8 m/s^2.
I hope this explanation helps you understand how to calculate the acceleration of the bar in this scenario.