Solving the Mass Sliding Problem with Increased Height h

[kirste]

My problem states, 2s is required for the mass to slide the distance d from a resting position. If the height h is increased by a factor of 4, while holding theta(angle) at 30, how long does it take the mass to slide the new distance d from rest?

height h =5.

My main question is (don't laugh please) When increasing by a factor of 4, is my height now 6.25? I know how to do the rest of the problem. g*sin*theta, then to d=1/2at^2, but I seem to have completely lost my brain regarding that part of the problem:)

Thanks

 

[Hootenanny]

An increase by a factor of 4 means that you multiply the original value by 4.

P.S. The Tutorial Sub-Forum is not for posting homework questions. Please post homework questions in the appropriate forum next time

 

[Moetasim]

for your question! It is completely understandable to have doubts or confusion when approaching a scientific problem. I am here to help clarify any misunderstandings and guide you through the process.

Firstly, let's address the issue of the height. When the height is increased by a factor of 4, it means that the new height is four times the original height. In this case, if the original height was h=5, then the new height would be 4*5=20. So, the new height is not 6.25, it is 20.

Now, let's move on to the problem at hand. The original problem states that it takes 2 seconds for the mass to slide the distance d from rest, with a height of h=5 and an angle of theta=30 degrees. The formula for this would be d=1/2*g*sin(theta)*t^2, where g is the acceleration due to gravity (9.8 m/s^2).

Now, if we increase the height by a factor of 4, the new height would be h=20. The question is asking for the time it would take for the mass to slide the same distance d from rest, with the new height of h=20 and the same angle of theta=30 degrees. The formula would still be the same: d=1/2*g*sin(theta)*t^2.

To solve for t, we can rearrange the formula to t=sqrt(2d/(g*sin(theta))). Plugging in the values, we get t=sqrt(2*1/(9.8*sin(30)))=0.253 seconds.

In summary, when the height is increased by a factor of 4, the new height is four times the original height. The time it takes for the mass to slide the distance d from rest with the new height would be 0.253 seconds. I hope this helps clarify any confusion. Good luck with your problem-solving!