Discovering Horizontal Acceleration: Newton's Law Question Solved

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I'm really stumped with this question.

A block is held against the front of a vertical wall of a railroud car. The coeffiecient of friction between the block and the wall is 0.4. When the train betgins to accelerate the block is released and begins to slide down the wall with an acceleration of 9.0m/s^2. What is the horizontal acceleration of the train?

I can't really show you much work that I've done because I can't really tell if i need to find the mass of the block..

I know that friction = 0.4*9.8*mass.

since the block has a normal force of mass*9.8 I don't knwo the normal force and I have no idea how to find it. someone give me a clue!

 

[Astronuc]

If the only force on the block was gravity, it should accelerate at g=9.8 m/s².

But the friction force is opposing it.

F_frict = mu * m_block * a, where a is the acceleration of the train.

The friction force must be = m(g-a_v), where a_v the block's vertical acceleration 9.0 m/s².

 

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how do you know that the friction is that?

 

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also i don't know know the mass of the block

 

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aslo the train is a force on it and i have ot find the acceleration of the train that would give that particular force so it slides down at 9.0m/s^2

 

[Doc Al]

Do it step by step. First assume that the applied force is just enough to hold the block against the wall if the train is not accelerating. What does that tell you about the applied force?

Now introduce acceleration. Write Newton's 2nd law for both the horizontal and vertical motion. You'll be able to solve for the horizontal acceleration.

 

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Do it step by step. First assume that the applied force is just enough to hold the block against the wall if the train is not accelerating. What does that tell you about the applied force?

Now introduce acceleration. Write Newton's 2nd law for both the horizontal and vertical motion. You'll be able to solve for the horizontal acceleration.

i'm sorry but i don't get what you mean

 

[Astronuc]

Try writing a vector diagram of the forces on the block.

Gravity is down, and the force of friction is opposite of gravity for a block sliding down, right? Friction opposes the direction of motion.

The friction force is related to the force imposed by the train - or rather it is related to the same mass (that of the block) and the acceleration of the train (which is what you are trying to find).

Think about the definition of the coefficient of friction.