Solving the Acceleration of a Bob Attached to a Train

In summary, The problem involves a bob of mass 0.35 kg attached to the roof of a train accelerating rightwards. The bob is inclined at an angle of 15° to the left. The acceleration of the train can be determined using Newton's 2nd law by analyzing horizontal and vertical components and taking into account the weight and tension of the string. Another question is then asked regarding equilibrium and the friction force from the wall. The equation W/2=Ytanθ is discussed and validated.
  • #1
jinhuit95
28
0

Homework Statement


A bob of mass 0.35 kg is attached by a string to the roof of a train that is accelerating rightwards and the mass is inclined at an angle of 15° to the left. Show that the acceleration of the train is 2.63 ms^-2.


The Attempt at a Solution


I don't know how to exactly start doing this because I don't know what concepts I should use here. Please help! :)
 
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  • #2
Use Newton's 2nd law. What forces act on the bob? Analyze horizontal and vertical components.
 
  • #3
How do you know what to use?? I was thinking of using mg sin θ in the first place.
 
  • #4
Start by drawing a free body diagram of the bob showing all forces acting on it. What forces act on the bob?
 
  • #5
Weight and tension of the string!
 
  • #6
jinhuit95 said:
Weight and tension of the string!
Right!

Now apply Newton's 2nd law. I suggest analyzing horizontal and vertical components separately.
 
  • #7
Alright I'll try! Can I ask you another question over here??
 
  • #8
jinhuit95 said:
Can I ask you another question over here??
Ask away.
 
  • #9
http://via.me/-2ostlh4
http://via.me/-2ostlh4
Here's the question and I did part of it and I don't know how to continue!
 
Last edited by a moderator:
  • #10
You took moments about the bottom end of the ladder, which is good. What about the other conditions for equilibrium?

(It's a bit difficult to read your work from the diagram, so write it out here if you want further critique.)
 
  • #11
Other condition will be the upward forces = downward forces?? Am I correct??
My working was W*0.5L cos θ = Y*L sin θ + f* L cos θ and that frictional force cause a moment too??
 
  • #12
jinhuit95 said:
Other condition will be the upward forces = downward forces?? Am I correct??
Yes.
My working was W*0.5L cos θ = Y*L sin θ + f* L cos θ and that frictional force cause a moment too??
Looks good.
 
  • #13
Doc Al said:
Yes.

Looks good.

so that means W= X+f?? And I just subt w into the above equation I did??
 
  • #14
jinhuit95 said:
so that means W= X+f?? And I just subt w into the above equation I did??
Yep.
 
  • #15
X=W
X=W/2 + W/2
Find value of W/2 in term of Y.
 
  • #16
azizlwl said:
X=W
Don't neglect the friction force from the wall.
 
  • #17
Taking as No friction on the wall,
If we take moment at the base,
(L/2)WCosθ=LYSinθ
W/2=YTanθ.

Then we can proof the equation.
 
  • #18
azizlwl said:
Taking as No friction on the wall,
If we take moment at the base,
(L/2)WCosθ=LYSinθ
W/2=YTanθ.

Then we can proof the equation.
But that's not the problem being discussed here. The wall is rough.
 
  • #19
Yes i make a mistake there.
With or without friction the equation still valid.
 
  • #20
azizlwl said:
With or without friction the equation still valid.
How can you say that?
 

FAQ: Solving the Acceleration of a Bob Attached to a Train

What is the concept of acceleration in physics?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction, and is typically measured in meters per second squared (m/s²).

How is acceleration calculated?

Acceleration is calculated by dividing the change in an object's velocity by the time it took for that change to occur. The formula for acceleration is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is the difference between constant and variable acceleration?

Constant acceleration refers to a situation where an object's acceleration remains the same throughout its motion. This can occur when there is a constant force acting on the object. Variable acceleration, on the other hand, means that the object's acceleration changes at different points during its motion.

How does a bob attached to a train experience acceleration?

A bob attached to a train experiences acceleration due to the train's motion. As the train accelerates or decelerates, the bob will also experience a change in velocity and therefore acceleration. This acceleration can be calculated using the formula mentioned earlier.

What factors can affect the acceleration of a bob attached to a train?

The acceleration of a bob attached to a train can be affected by various factors, such as the mass of the bob, the force applied by the train, and the friction between the bob and the train. Other external forces, such as air resistance, can also impact the acceleration of the bob.

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