# The laws of motion-a toy with a accelerating car

1. Dec 25, 2013

### haha1234

1. The problem statement, all variables and given/known data

A car accelerates down a hill,going form rest to 30.0m/s in 6.00s.A toy inside the car hangs by a string form he car's ceiling.The ball in the figure represents the toy,of mass 0.100 kg.The acceleration id such that the string remains perpendicular to the ceiling.Determine (a) the angle θ and (b) the tension in the string.

2. Relevant equations

3. The attempt at a solution
Are there any mistakes?I cannot find the correct answer.
Tcosθ=mg
Tocsθ=0.1X9.8=0.98----1
Tsinθ=ma
Tsinθ=0.1x30/6=0.5-----2
Then solve 1 and 2

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Last edited: Dec 25, 2013
2. Dec 25, 2013

### ehild

Tsinθ is the horizontal component of the tension in the string. But the car (and the toy together with it ) does not accelerate edit: exactly in the horizontal direction.

Draw the forces acting on the toy and find the components parallel and normal to the slope.

ehild

Last edited: Dec 25, 2013
3. Dec 25, 2013

### haruspex

∑F=ma, right? Your equation is ∑F=0. Is the toy accelerating?

4. Dec 25, 2013

### haha1234

Why the toy does not accelerate in the horizontal direction?
The question state that the car went from rest to 30.0m/s in 6.00s.
Are there anything wrong in my free body diagram?

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5. Dec 25, 2013

### ehild

Sorry, I should have written that the acceleration of the toy is not horizontal. Its acceleration has both horizontal and vertical components. What is the direction of the acceleration?

ehild

6. Dec 25, 2013

### haha1234

Is the weight of the toy accounts for the acceleration?

7. Dec 25, 2013

### ehild

Is weight the only force acting on the toy?

ehild

8. Dec 25, 2013

### haha1234

Are the weight and the tension both accounts for the acceleration?

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9. Dec 25, 2013

### ehild

Yes. (But your drawing is not clear to me. You can take that the top of the car is parallel to the road. )

ehild

10. Dec 26, 2013

### haha1234

Finally I've found these two equation.
Tsinθcosθ+Wsinθcosθ=ma---1
Tcosθ=W----2
Are they correct?

11. Dec 26, 2013

### haruspex

No, neither.
What forces act on the toy, and in what directions?
In what direction is the resultant acceleration?

12. Dec 27, 2013

### haha1234

Why Tcos≠mg?

13. Dec 27, 2013

### ehild

Why do you think it is????

If it was true that toy would not accelerate in vertical direction. But it accelerates down along the slope, together with the car, its acceleration has both horizontal and vertical components.

A drawing would be much help. Draw all forces acting on the toy and also the vector of its acceleration.

ehild