Acceleration on an Incline: Calculating Net Acceleration and Final Speed

In summary, the record for grass skiing was set and it took Spinka 6.60 s to reach his top speed after starting from rest down a 34 degree incline with a coefficient of friction of 0.198. The magnitude of Spinka's net acceleration was 5.486 m/s2. To find his speed after 6.60 s, the formula Fnet = ma = mg(sinθ) - μmg(cosθ) was used and then solved for a, with the mass (m) cancelling out. It is also important to use kinematics to find the speed. Through this conversation, it is evident that the person providing the summary is knowledgeable in physics and is willing to help others.
  • #1
RingWraith2086
5
0
Question: The record for grass skiing was set blah blah blah. Suppose it took Spinka 6.60 s to reach his top speed after he started from rest down a slope with a 34 degree incline. If the coefficient of friction between the skis and the grass was 0.198, what was the magnitude of Spinka's net acceleration? What was his speed after 6.60 s?

Here's what I've done:
I thought a=g(sinTheta)
Which gives me
a = 9.81(sin34)
a = 5.486 m/s2,
which isn't right. What am I doing wrong?
 
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  • #2
Don't forget the friction:

[tex] F_{\rm net} = ma = mg\sin\theta - \mu mg\cos\theta [/tex]

Solve for a (you'll see that m cancels out) and then use kinematics to get the speed part.
 
  • #3
Well you just seem to know everything don't you? Maybe once I get through a quarter of physics I'll be able to help people too. Thanks once again.
 
  • #4
Originally posted by RingWraith2086
Well you just seem to know everything don't you? Maybe once I get through a quarter of physics I'll be able to help people too. Thanks once again.

If only I did... Well, I'm glad I knew enough to help you here. It's also good to hear your willing to help when you can too. Keep up the good work.
 

1. What is acceleration on an incline?

Acceleration on an incline is the rate of change of velocity of an object moving on an inclined surface. It is a measure of how quickly the object's speed or direction is changing.

2. How does acceleration on an incline differ from acceleration on a flat surface?

Acceleration on an incline is affected by both gravity and the angle of the incline, whereas acceleration on a flat surface is only affected by gravity. This means that on an incline, the object will accelerate both downwards due to gravity and along the incline due to the angle.

3. How is acceleration on an incline calculated?

Acceleration on an incline can be calculated using the formula a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (usually 9.8 m/s²), and θ is the angle of the incline.

4. What factors can affect acceleration on an incline?

The two main factors that can affect acceleration on an incline are the angle of the incline and the mass of the object. The steeper the incline, the greater the acceleration, and the heavier the object, the slower the acceleration.

5. How can acceleration on an incline be used in real-life situations?

Understanding acceleration on an incline can be useful in many real-life situations, such as designing roller coasters and other amusement park rides, calculating the speed and trajectory of objects rolling down hills, and determining the forces acting on objects on slopes or ramps.

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