# Distance up and incline plane

• am08
In summary, to find the distance up an incline plane for a block with initial velocity sliding down and then projected up the same plane, you need to take into account the work done by the force of gravity. The correct equation is: KEi + Wnc + Wg = KEf = 0.5•m•vi2 + F•d•cosθ + F•d•sinθ = m•g•hf. Using this equation, the block in this scenario will move up the incline for a distance of 0.24 meters before coming to rest.
am08
[SOLVED] Distance up and incline plane

A block with mass m = 11.5 kg slides down an inclined plane of slope angle 24.5 o with a constant velocity. It is then projected up the same plane with an initial speed 3.75 m/s. How far up the incline will the block move before coming to rest?

Equation: KEi + Wnc = KEf = 0.5•m•vi2 + F•d•cos = m•g•h f

(0.5*11.5*3.75^2) + (11.5*-9.8*cos25.4)d = (11.5*9.8)hf

80.9 - 102.6d = 112.7hf

hf = sin24.5 d = .415d

80.9 - 102.6d = 46.8d

d = .54 m

What did I do wrong

?You did not take into account the work done by the force of gravity. The work done by gravity is W = F·d·sinθ, where F is the force of gravity, d is the displacement and θ is the angle of the inclined plane. Therefore, the equation should be: KEi + Wnc + Wg = KEf = 0.5•m•vi2 + F•d•cosθ + F•d•sinθ = m•g•hf (0.5*11.5*3.75^2) + (11.5*-9.8*cos25.4)d + (11.5*-9.8*sin25.4)d = (11.5*9.8)hf80.9 - 205.2d = 112.7hfhf = sin24.5 d = .415d 80.9 - 205.2d = 46.8dd = .24 m

Your calculations seem correct. However, it is always a good idea to double check your work and make sure all units are consistent. Also, it is important to clearly define your reference frame and direction of motion for the block. Additionally, it would be helpful to provide more context and information about the problem, such as the height of the incline and whether or not there is any friction present. This can help to ensure that your solution is accurate and relevant to the given problem.

## What is distance up an incline plane?

Distance up an incline plane is the distance a body must travel to reach a certain height on an inclined plane, taking into account the angle of inclination and the starting and ending heights.

## How is distance up an incline plane calculated?

Distance up an incline plane is calculated using the formula d = (h2-h1)/sinθ, where d is the distance traveled, h1 is the starting height, h2 is the ending height, and θ is the angle of inclination.

## What factors affect the distance up an incline plane?

The distance up an incline plane is affected by the angle of inclination, the height difference between the starting and ending points, and the force applied to move the body up the incline.

## How does the angle of inclination impact the distance up an incline plane?

The steeper the angle of inclination, the shorter the distance up the incline plane will be. This is because the force needed to move the body up the incline increases as the angle gets steeper.

## What is the difference between distance up an incline plane and distance on a flat surface?

Distance up an incline plane takes into account the vertical height difference between the starting and ending points, while distance on a flat surface only considers the horizontal distance traveled. Additionally, the force needed to move a body up an incline plane is greater than that needed to move it across a flat surface, resulting in a longer distance traveled.

• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
33
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
5K
• Introductory Physics Homework Help
Replies
2
Views
923
• Introductory Physics Homework Help
Replies
1
Views
989
• Introductory Physics Homework Help
Replies
68
Views
9K