The laws of motion-a toy with a accelerating car

[haha1234]

Homework Statement

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.

Homework Equations

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

 

[ehild]

Homework Statement

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.

Homework Equations

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

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

 

[haruspex]

Tcosθ=mg

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

 

[haha1234]

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

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

ehild

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?

 

[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

 

[haha1234]

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

Is the weight of the toy accounts for the acceleration?

 

[ehild]

Is weight the only force acting on the toy?

ehild

 

[haha1234]

Is weight the only force acting on the toy?

ehild

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

 

[ehild]

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

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

ehild

 

[haha1234]

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

ehild

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

 

[haruspex]

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

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

 

[haha1234]

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

Why Tcos≠mg?

 

[ehild]

Why Tcos≠mg?

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