Questions on projectiles & Newton's laws of motion

In summary, the conversation discusses the topic of projectiles and Newton's laws of motion, specifically looking at the motion of a projectile with drag that is proportional to the square of velocity. The conversation also mentions adding in a variable wind or constant applied force, as well as a more complicated scenario involving a particle attached to two springs. The conversation concludes with a request to derive the equations of motion for a spherical simple pendulum.
  • #1
almirza
11
0
hi there

falks i need some hard questions on projectiles & Newton's laws of motion...
 
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  • #2
for starters think about the motion of a projectile with drag that is proportional to the square of velocity. Express the position in terms of cartesian coorinates and then transform to cylindrical. Comment on what set is better for a given set initial conditions.

To make things more complicated add invariable wind (or a constant applied force in an inertial direction)

Another complicated problem is to consider a particle attached to 2 springs. Each spring is connected to the ceiling and makes some angle between the horizontal and the particle. Each spring has a different spring constant. Find the equations of motion of the particle. Plot the phase between the x and y coordinates. Design spring 1 such that the particle will retrace its path with each cycle. Determine the maximum amplitide of the particles displacement from the equilibrium position. Assume m = 1 kg, theta1 = 30 deg, theta 2 = 60 deg, k2/k1 = sqrt(2). for the EOMs assume k1 = 1 N/m.

Derive the equations of motion for a spherical simple pendulum. (This is a pendulum that is free to rotate is both the horizontal and vertical planes)
 
  • #3


1. How does the mass of an object affect its motion when launched as a projectile?
2. Can a projectile ever reach a state of constant velocity? Why or why not?
3. How does air resistance affect the trajectory of a projectile?
4. Is it possible for a projectile to have a curved path without the influence of external forces?
5. How does the angle of launch affect the range of a projectile?
6. Can a projectile's initial velocity and angle of launch be manipulated to achieve the same range?
7. How do Newton's laws of motion explain the motion of a projectile?
8. Can a projectile's motion be influenced by more than one force?
9. How does the height of a projectile's launch affect its time of flight?
10. Can a projectile's motion be accurately predicted without taking into account air resistance?
 

Related to Questions on projectiles & Newton's laws of motion

1. How do Newton's laws of motion apply to projectiles?

Newton's laws of motion apply to projectiles because projectiles are objects that are in motion and are subject to the same laws as any other object in motion. This includes the first law, which states that an object will remain in motion unless acted upon by an external force, the second law, which states that the acceleration of an object is directly proportional to the net force acting on it, and the third law, which states that for every action, there is an equal and opposite reaction.

2. What is the difference between a projectile and a regular object in motion?

The main difference between a projectile and a regular object in motion is that a projectile is an object that is only acted upon by gravity, while a regular object can also experience other forces such as friction or air resistance. Additionally, a projectile follows a curved path due to the influence of gravity, while a regular object may follow a straight path.

3. How does the angle of projection affect the trajectory of a projectile?

The angle of projection, or the angle at which a projectile is launched, plays a crucial role in determining the trajectory of the projectile. The ideal angle of projection for maximum distance is 45 degrees, as this angle allows the projectile to travel the farthest before hitting the ground. Any angle less than 45 degrees will result in a shorter distance, while angles greater than 45 degrees will result in a higher arc and also a shorter distance.

4. Can you explain the concept of air resistance in relation to projectiles?

Air resistance, also known as drag, is a force that acts in the opposite direction of the motion of a projectile. This force increases as the speed of the projectile increases. In the absence of air resistance, a projectile would continue to move at a constant speed and direction. However, with the presence of air resistance, the projectile experiences a deceleration, causing it to eventually come to a stop.

5. How can we calculate the trajectory of a projectile using Newton's laws of motion?

To calculate the trajectory of a projectile using Newton's laws of motion, we can use the equations of motion, which are derived from Newton's second law. These equations take into account the initial velocity, angle of projection, and acceleration due to gravity to determine the position, velocity, and time of a projectile at any point in its trajectory. By plugging in different values for these variables, we can calculate the trajectory of a projectile and predict where it will land.

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