Deceleration of rocks sliding up a hill

In summary, the conversation discusses the concepts of cosθ and sinθ in relation to the two dimensions of acceleration and how to resolve their components using a free body diagram. The conversation also raises a question about a possible error in the given answer, as well as clarifying the directions of positive and negative acceleration. A diagram accompanying the problem would provide further clarity.
  • #1
jamiebean
55
3
Homework Statement
attached below
Relevant Equations
kinetic coefficient x normal force= kinetic energy
螢幕截圖 2020-05-22 下午7.38.43.png


i have no idea how did the answer come in conclusion...i guess that cosθ and sinθ is referring to the 2 dimensions of the acceleration ? but how? and why?
 
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  • #2
jamiebean said:
Homework Statement:: attached below
Relevant Equations:: kinetic coefficient x normal force= kinetic energy

i guess that cosθ and sinθ is referring to the 2 dimensions of the acceleration ?
Yes. Do as they suggest and draw a FBD. That will help you to resolve the components.

BTW, I think the answer given is wrong -- it has a sign error, no?
 
  • #3
There are two terms to the acceleration because there are two separate forces opposing its uphill motion. What are these two forces?

Edit: Rats! @berkeman beat me to it.
 
  • #4
berkeman said:
BTW, I think the answer given is wrong -- it has a sign error, no?
Unless by "base" they mean the top of the hill? That would usually be referred to as the "top" or "crest" of the hill, not the "base", IMO... Is there a diagram that goes with this problem?
 
  • #5
berkeman said:
Unless by "base" they mean the top of the hill? That would usually be referred to as the "top" or "crest" of the hill, not the "base", IMO... Is there a diagram that goes with this problem?
One one hand, the question does not specify whether the positive direction is uphill or downhill so the number for the acceleration can have either sign. On the other hand, the question may have adopted the convention that "positive" means "in the direction of the velocity" which means the number must be negative. The question would have no ambiguity if it asked for the magnitude or if it specified which way is positive.
 
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1. What causes rocks to decelerate while sliding up a hill?

The main cause of deceleration for rocks sliding up a hill is the force of gravity acting against the motion of the rock. As the rock moves up the hill, it must overcome the downward pull of gravity, causing it to slow down.

2. How does the angle of the hill affect the deceleration of rocks?

The steeper the angle of the hill, the greater the force of gravity acting against the motion of the rock. This results in a higher deceleration rate for the rock as it slides up the hill.

3. Can the type of rock affect the deceleration rate while sliding up a hill?

Yes, the type of rock can have an impact on the deceleration rate while sliding up a hill. Rocks with a rougher surface or more irregular shape may experience more friction as they move up the hill, causing them to decelerate at a faster rate.

4. Is there a maximum speed that a rock can reach while sliding up a hill?

Yes, there is a maximum speed that a rock can reach while sliding up a hill. This is due to the force of gravity, which will eventually slow the rock down to a complete stop if the hill is steep enough.

5. Can external factors, such as wind or water, affect the deceleration of rocks sliding up a hill?

External factors, such as wind or water, can impact the deceleration of rocks sliding up a hill. Wind can create additional resistance against the rock, causing it to decelerate at a faster rate. Water can also add weight to the rock, making it more difficult to move up the hill and resulting in a slower deceleration rate.

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