Solving for Time Taken to Slide Down Roof

  • Thread starter Vanessa23
  • Start date
  • Tags
    Sliding
In summary, the ball started at a height of 12.5 meters and rolled to the edge of a roof which is 7 meters high. It rolled a horizontal distance of 6 meters and a vertical distance of 5.5 meters. Using the given values, the velocity of the ball was calculated to be 9.84 m/s and the acceleration was 3.39 m/s^2. However, there is a lack of information about the ball's characteristics, and it is unclear if the question is referring to sliding or rolling motion.
  • #1
Vanessa23
41
0

Homework Statement


a ball started at a height of 12.5 meters and rolled to the edge of a roof which is at 7 meters. Using a^2+b^2=c^2 we know it rolled a distance of 8.14 meters on the roof because it rolled a horizontal distance of 6m and a vertical distance of 5.5m. Find the time it rolled down the roof. The roof makes a 40deg angle with the horizontal and coeff of friction is .388.

Homework Equations


Potential E=KE+Ffriction
mg*distance*sin(theta)=.5mv^2+(coeff of friction)*mgcos(theta)*distance down roof
acceleration=g*sin(theta)-g*(coeff. of friction)*cos(theta)
V=Vo+at

The Attempt at a Solution



8.14*g*sin(40)=.5v^2+.388*g*cos(40)*(8.14)
v=9.84m/s

a=g*sin40)-g*.388cos(40)
a=3.39m/s^2

9.84=3.39t
t=2.90 seconds
 
Last edited:
Physics news on Phys.org
  • #2
Vanessa23 said:
a ball started at a height of 12.5 meters and rolled to the edge of a roof ...
... we know it rolled a distance of 8.14 meters on the roof because it rolled a horizontal distance of 6m and a vertical distance of 5.5m. Find the time it rolled down the roof. ...

What you have solved is for sliding down the roof whereas, the question has reiterated the term rolling. I think, question has been manipulated, in your own words!

The attempt is correct, method-wise, if it is sliding. So, have you written 'sliding' incorrectly?
If it is indeed 'rolling', one information is missing: information about the ball? Assuming a spherical ball (as most of them are), is it solid or hollow? Have you missed that?
 
  • #3


As a scientist, it is important to provide a clear and concise explanation of how you arrived at your solution. In this case, the problem can be solved by using the equations for potential energy, kinetic energy, and frictional force, as well as the given information about the angle of the roof and the coefficient of friction.

First, we can use the equation for potential energy (PE=mgh) to find the initial potential energy of the ball at the height of 12.5 meters. This can then be equated to the final kinetic energy (KE=1/2mv^2) plus the work done by friction (Ffriction = μmgd*cosθ), where μ is the coefficient of friction, m is the mass of the ball, g is the acceleration due to gravity, and d is the distance the ball rolls down the roof.

Next, we can use the given information about the angle of the roof and the distance the ball rolled to find the horizontal and vertical components of the distance traveled. Using the Pythagorean theorem (a^2+b^2=c^2), we can calculate the total distance traveled by the ball on the roof.

Then, we can use the equation for acceleration (a=g*sinθ-μg*cosθ) to find the acceleration of the ball as it rolls down the roof. This can be substituted into the equation for velocity (V=Vo+at) to find the final velocity of the ball at the edge of the roof.

Finally, we can use the equation for velocity to find the time taken for the ball to roll down the roof, given the initial velocity (which is assumed to be 0 since the ball starts at rest) and the final velocity found in the previous step.

In this way, we can use the given information and equations to solve for the time taken for the ball to slide down the roof, which is approximately 2.90 seconds.
 

1. How do you calculate the time taken to slide down a roof?

The time taken to slide down a roof can be calculated using the formula t = √(2h/g), where t is the time in seconds, h is the height of the roof in meters, and g is the acceleration due to gravity (9.8 m/s²).

2. What factors affect the time taken to slide down a roof?

The time taken to slide down a roof can be affected by several factors, including the height of the roof, the angle of inclination, the presence of friction, and the weight and shape of the object sliding down.

3. How does the angle of inclination affect the time taken to slide down a roof?

The steeper the angle of inclination, the faster an object will slide down a roof. This is because a steeper angle will result in a greater component of the object's weight acting parallel to the roof, increasing its acceleration.

4. How does friction affect the time taken to slide down a roof?

Friction between the object and the roof will slow down the sliding motion, resulting in a longer time taken to slide down the roof. The amount of friction depends on the materials and surfaces involved.

5. Can the time taken to slide down a roof be reduced?

Yes, the time taken to slide down a roof can be reduced by increasing the angle of inclination, reducing friction (e.g. by using a lubricant), or decreasing the weight of the object sliding down. However, safety precautions should always be taken when attempting to reduce the time taken to slide down a roof.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
2
Replies
59
Views
4K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
740
  • Introductory Physics Homework Help
Replies
2
Views
804
Back
Top