The laws of motion-a toy with a accelerating car

In summary: 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.
  • #1
haha1234
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0

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.:cry:
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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  • #2
haha1234 said:

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.:cry:
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
 
Last edited:
  • #3
haha1234 said:
Tcosθ=mg
∑F=ma, right? Your equation is ∑F=0. Is the toy accelerating?
 
  • #4
ehild said:
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?
 

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  • #5
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
ehild said:
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?
 
  • #7
Is weight the only force acting on the toy?

ehild
 
  • #8
ehild said:
Is weight the only force acting on the toy?

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

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  • #9
haha1234 said:
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
 
  • #10
ehild said:
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?
 
  • #11
haha1234 said:
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?
 
  • #12
haruspex said:
No, neither.
What forces act on the toy, and in what directions?
In what direction is the resultant acceleration?

Why Tcos≠mg?
 
  • #13
haha1234 said:
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
 
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What are the three laws of motion?

The three laws of motion, also known as Newton's laws of motion, are the basic principles that govern the motion of objects. They are:
1. The law of inertia: An object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an external force.
2. The law of acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
3. The law of action and reaction: For every action, there is an equal and opposite reaction.

How do these laws apply to a toy with an accelerating car?

The first law of motion applies to the toy car when it is at rest on a surface. It will not move until a force is applied to it, such as pushing it with your hand. The second law of motion applies to the car's acceleration - the harder you push, the faster it will accelerate. The third law of motion can be seen when the car collides with another object, causing both objects to experience equal and opposite forces.

What factors affect the motion of the toy car?

The motion of the toy car can be affected by several factors, including the force applied to it, the mass of the car, and the surface it is moving on. Friction between the car and the surface can also affect its motion, as well as any external forces acting on it, such as air resistance or gravity.

How can you change the motion of the toy car?

The motion of the toy car can be changed by varying the force applied to it, changing its mass, or altering the surface it is moving on. For example, a smoother surface will result in less friction and a faster acceleration. Additionally, changing the direction or angle of the force applied can also change the car's motion.

Why are the laws of motion important to understand?

The laws of motion are important because they help us understand and predict the behavior of objects in motion. They are the foundation of mechanics and have many practical applications, such as designing vehicles, predicting the motion of celestial bodies, and understanding the forces acting on structures. They also allow us to explain and analyze the world around us in a more scientific and precise manner.

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