How Do You Calculate Speed at the Bottom of a Hill Considering Friction?

  • Thread starter lonlyincolleg
  • Start date
  • Tags
    Hill Speed
In summary, a bike traveling at 11 m/s down a hill with a hill of 10 m height and 100 m length will experience a force of 20 newtons of friction. This will cause the bike to slow down to 5 m/s.
  • #1
lonlyincolleg
3
0
Speed at the bottom of a hill - Please help!

Homework Statement


Bike (mass 40kg) traveling down a hill. Speed at the top of the hill is 5.0 m/s. The hill is 10m high and 100m long. Force of friction is 20N, what is the speed at the bottom?


Homework Equations


The only formula I've tried is v(final) = Sq. rt. of 2gy(initial). I don't know what y is, where friction plays into this and obviously I'm not getting the answer. Please help!


The Attempt at a Solution


I have converted the units to kg, and m, and drawn a picture. I know that the answer is 11 m/s but there isn't a formula or very similar problem in my book. (The only similar problem doesn't account for friction so I don't really know where to begin.
 
Physics news on Phys.org
  • #2


lonlyincolleg said:

Homework Statement


Bike (mass 40kg) traveling down a hill. Speed at the top of the hill is 5.0 m/s. The hill is 10m high and 100m long. Force of friction is 20N, what is the speed at the bottom?


Homework Equations


The only formula I've tried is v(final) = Sq. rt. of 2gy(initial). I don't know what y is, where friction plays into this and obviously I'm not getting the answer. Please help!


The Attempt at a Solution


I have converted the units to kg, and m, and drawn a picture. I know that the answer is 11 m/s but there isn't a formula or very similar problem in my book. (The only similar problem doesn't account for friction so I don't really know where to begin.

Conservation of mechanical energy:

[tex]K_i+U_i-\vec{W}=K_f+U_f[/tex].
 
  • #3


asleight said:
Conservation of mechanical energy:

[tex]K_i+U_i-\vec{W}=K_f+U_f[/tex].

W should be positive, not negative, and it's the work done by friction.
 
  • #4


You will have to know the distance traveled by the bike to know the amount of work done by friction. Find that out from your picture. After that use that energy is conservated as suggested. Be wary of how you define your friction. Look at the dimensions of your terms, they should always correspond. The total energy before (at the top of the hill) should equal the total energy after (including the work done by friction during the ride).
 

FAQ: How Do You Calculate Speed at the Bottom of a Hill Considering Friction?

What is the speed at the bottom of a hill?

The speed at the bottom of a hill depends on several factors, including the initial speed of the object, the angle of the hill, and the presence of any external forces such as friction or air resistance. It is not possible to determine a single value for the speed at the bottom of a hill without knowing these variables.

How does the angle of the hill affect the speed at the bottom?

The angle of the hill has a significant impact on the speed at the bottom. A steeper hill will result in a higher speed at the bottom due to the acceleration of gravity. On the other hand, a shallower hill will result in a lower speed due to a lower gravitational pull.

Does the initial speed of the object affect the speed at the bottom of a hill?

Yes, the initial speed of the object will affect the speed at the bottom of a hill. If the object has a higher initial speed, it will have a higher speed at the bottom of the hill due to the conservation of energy. However, other factors such as air resistance may also play a role in determining the final speed.

How does friction affect the speed at the bottom of a hill?

Friction can have a significant impact on the speed at the bottom of a hill. If there is a lot of friction, the object will slow down as it moves down the hill, resulting in a lower speed at the bottom. However, if there is minimal friction, the object may maintain a higher speed at the bottom.

Can the speed at the bottom of a hill be calculated?

Yes, the speed at the bottom of a hill can be calculated using the principles of physics such as the equations of motion and conservation of energy. However, accuracy may vary depending on the accuracy of the variables used in the calculation and any external factors that may affect the speed.

Similar threads

Energy calculations for a skier on a hill
Replies
6
Views
6K
Find the speed of the biker at the bottom of the hill
2
Replies
38
Views
3K
Finding the Formula for Speed and Distance on an Icy Hill
Replies
11
Views
2K
Speed skier travelling up a hill
Replies
7
Views
3K
Help Me Hill Height for 35kg Child on 5kg Sled
Replies
6
Views
1K
What is the deceleration of a snowboarder going up a 5.0° slope?
Replies
2
Views
13K
A cylinder of snow rolls down a hill gathering more snow -- calculate its speed
2
Replies
39
Views
2K
How high can it coast up the hill, if you neglect friction?
Replies
1
Views
4K
Sledding Down a Hill: Calculating Friction and Velocity
Replies
31
Views
3K
How to calculate the kinematics of an object pushed up an inclinex plane?
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top