What is the path of the ball's movement in different scenarios?

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In summary, A ball with radius r and mass m enters a semispherical shell with radius R and coefficient of friction µ. The shell is on a moving car with circular path of radius a. Three scenarios are given: (A) the car and shell have zero velocity, (B) the shell rotates around its z-axis with constant angular velocity w1, and (C) the shell rotates with w1 and the car moves with constant angular velocity w2. The task is to determine the path of the ball's movement in each scenario.
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hi friends , please help me to solve this problem , THANKS :

A ball with radius r and mass m with angel 30 with horizon and with velocity V, according to figure, enters to a semispherical shell with radius R and the coefficient of friction between semispherical shell and ball is µ . This semispherical shell is in the Car moving at the circular path with radius a .assume that the semispherical shell is without any linear or lateral movement on the car:

A: assume that the velocity of car and the semispherical shell is zero, and determine the path of the Ball’s movement.

B: assume that the semispherical shell rotate about its z-axe with constant angular velocity of w1 and determine the path of the Ball’s movement.

C: assume that the semispherical shell rotate about its z-axe with angular velocity of w1, and the car moves in circular path with constant angular velocity of w2. Determine the path of the Ball’s movement.
 

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No help ??
 

FAQ: What is the path of the ball's movement in different scenarios?

1. What is Dynamics?

Dynamics is the branch of mechanics that studies the motion of objects and systems under the influence of forces. It involves the study of how objects move, why they move, and what factors affect their motion.

2. How do forces affect an object's motion?

Forces can cause an object to change its speed, direction, or both. The magnitude and direction of the force determine how the object will move. If the forces are balanced, the object will remain at rest or continue to move at a constant velocity. If the forces are unbalanced, the object will accelerate in the direction of the net force.

3. What is Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental laws that describe how objects move in response to forces. The first law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an unbalanced force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

4. How do we measure and calculate forces in dynamics?

Forces are measured in units called Newtons (N). To calculate the net force acting on an object, we use the formula F=ma, where F is the net force, m is the mass of the object, and a is the acceleration. Forces can also be represented by vectors, which show the magnitude and direction of the force.

5. What are some real-life applications of dynamics?

Dynamics has many real-life applications, including the design of structures, machines, and vehicles. It is also used in sports and games, such as calculating the trajectory of a ball in baseball or the motion of a car in a racing game. Additionally, dynamics is crucial in understanding natural phenomena such as the motion of planets and other celestial bodies.

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