Speed of an object sliding down

In summary, an object of mass 2 kg slides down a frictionless track from a height of 10 m, except for the horizontal range between points A and B where there is a constant friction force of 10 N. The final speed of the object at point B can be found by using the equation KE = 1/2 mv^2 and accounting for the work done by friction, which is equal to the change in potential energy (mgh) minus the frictional force. The result of this calculation should be -100 J, which can then be solved for the final speed of the object.
  • #1
AlexanderIV

Homework Statement


An object of mass m=2 kg slides down on a track from a height of h = 10 m. The track is frictionless except the horizontal range between the points A and B. The friction force is constant between A and B. What is the speed of the object at point B if the magnitude of the friction force between A and B is f = 10 N (take g = 10 m/s2) .
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Homework Equations


F = m (dv / dt)
KE = 1/2 mv^2

The Attempt at a Solution



The potential energy while sliding down would be U=mgh=2x10x10=200 J[/B]
I have no idea what to do after this point.
 

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  • #2
AlexanderIV said:
Relevant equations
What equation connects work and force?
 
  • #3
haruspex said:
What equation connects work and force?
W = Fdcosθ
 
  • #4
AlexanderIV said:
W = Fdcosθ
Can you apply that to the strip AB?
 
  • #5
If I apply it would be W = Fdcosθ = (mgsinθ)x10xcos0= (2x10xsin0)x10x1=0 but that does not make sense to me.
 
  • #6
AlexanderIV said:
If I apply it would be W = Fdcosθ = (mgsinθ)x10xcos0= (2x10xsin0)x10x1=0 but that does not make sense to me.
What force affects the speed?
 
  • #7
The gravitational force affects the speed. Then it should be W = Fdcosθ = (mg)dcosθ = (2x10)x10x1 = 200 J?
 
  • #8
AlexanderIV said:
The gravitational force affects the speed.
No, I mean along the strip AB.
 
  • #9
haruspex said:
No, I mean along the strip AB.

The friction force.
 
  • #10
AlexanderIV said:
The friction force.
So write the energy equation in relation to that.
 
  • #11
W = (mgsinθ - kmg)dcosθ = (2x10x0 - kx2x10)x10x1 = (0-20k)x10 = -200k J ?
 
  • #12
AlexanderIV said:
W = (mgsinθ - kmg)dcosθ = (2x10x0 - kx2x10)x10x1 = (0-20k)x10 = -200k J ?
I assume k represents the coefficient of kinetic friction, but you are not given that. You don't need it because you are given the actual frictional force.
 
  • #13
Then it should be -100 J but I don't know how I could relate that to the speed.
 
  • #14
AlexanderIV said:
Then it should be -100 J but I don't know how I could relate that to the speed.
You don't know how a change in energy relates to a change in speed? You quoted an expression for KE.
 
  • #15
-100 = 1/2mv^2 => -100=v^2 => -100=v^2

But this is not possible, is it?
 
  • #16
AlexanderIV said:
-100 = 1/2mv^2 => -100=v^2 => -100=v^2

But this is not possible, is it?
It started with some energy. The work done by friction is only a deduction from that.
 
  • #17
It started with potential energy, so W = Fdcosθ = (mgh - f)dcosθ = (200 - 10)10 = 190 x 10 = 1900 J?
 
  • #18
AlexanderIV said:
mgh - f
That makes no sense. You are subtracting a force from an energy term.
What energy did it gain by descending, and what does it lose to friction?
 

Related to Speed of an object sliding down

1. What factors affect the speed of an object sliding down?

The speed of an object sliding down is affected by several factors, including the angle of the slope, the mass and shape of the object, and the presence of any external forces such as friction or air resistance. Additionally, the surface of the slope and the material of the object can also impact its speed.

2. How does the angle of the slope affect the speed of an object sliding down?

The steeper the slope, the faster the object will slide down. This is because a steeper slope provides a greater vertical drop, allowing the object to accelerate more quickly due to the force of gravity.

3. Does the mass of an object affect its speed while sliding down?

Yes, the mass of an object does affect its speed while sliding down. Objects with a greater mass have a greater inertia, meaning they require more force to accelerate. This results in a slower speed compared to objects with less mass.

4. How does friction affect the speed of an object sliding down?

Friction can significantly impact the speed of an object sliding down. Friction is a force that resists motion, so the presence of friction on the surface of the slope can slow down the object's speed. However, if the object is on a surface with low friction, it will slide down faster.

5. What is the difference between static and kinetic friction in relation to an object sliding down?

Static friction is the force that resists motion when an object is at rest. In the case of an object sliding down a slope, static friction would prevent the object from moving until enough force is applied to overcome it. Kinetic friction, on the other hand, is the force that resists motion when an object is already in motion. As the object slides down the slope, kinetic friction will act against its motion and cause it to slow down.

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