Best Canon :D

In order to make a perfect canon which has the greatest horizontal range covered, one needs to keep in mind the angle of the barrel which must be 45 degrees above the horizontal. This angle would be perfect in order to make the canon go as further as it could. We can use the following formula in order to determine the angle at which the canon covers the maximum range:

R = V²sin(2θ)/g

Using this formula, we can determine the value of θ that will maximize the value of sin(2θ), which will maximize the range of the projectile since v and g do not change. The maximum value of sin(2θ) is 1, which occurs at sin(90). Therefore the value of θ must be 45 degrees above the horizontal. 

Newton's Problems

1: Equilibriums
Assumption:
-Positive axes
-∑F = 0 ( ∑Fx = 0 , ∑Fy = 0), a = 0
- no friction
- no air resistance
- rope is weightless

When calculating, divide all the force to x-axis and y-axis,
Fx = max        Fy = may
Fx = 0              Fy = 0

2: Inclines
a) object is at rest
Assumptions:
- postive is along the incline direction
- ∑F = 0, a = 0
- no air resistance
- FN is perpendicular to incline
                     ∑F = ma 
∑Fx = max                ∑F = may
∑Fx = 0                       ∑F = 0
Fgx - f = 0                 FN - Fgy = 0

b) object is moving
Assupmtions:
- positive is along the incline direction
- ∑Fy = 0 , ∑F is not equal to 0
- no air resistance
- FN is perpendicular to incline
use the same method of calculation as when object is at rest

3: Pulley
Assumptions:
- polley is frictionless
- rope is frictionless and weightless
- no air resistance
- 2 systems (2 FBDs)
- T1 = T2
- a of the system is the same (ay1 = ay2)

Note that ∑Fx = 0 for both objects
Do the calculation by dividing the foerces into x and y.
4: Trains
Assumptions:
- Use 3FBDs  to find T
- no air resistance
- ay = 0
- cables are weightless
- positive is in the direction of a
- a is consistant

Assume the whole system as an object to calculate the acceleration
Then use 3 FBDs to find tension amoung the masses

Projectile Motion

Projectile motion is a special case of two dimensional motion with constant acceleration. Here, force due to gravity moderates linear motion of an object thrown at certain angle to the vertical direction. The resulting acceleration is a constant, which is always directed in vertically downward direction.

There is a very useful aspect of two dimensional motion that can be used with great effect. Two dimensional motion can be resolved in to two linear motions in two mutually perpendicular directions : (i) one along horizontal direction and (ii) the other along vertical direction. The linear motion in each direction can, then, be analyzed with the help of equivalent scalar system, in which signs of the attributes of the motion represent direction. The x-axis in the projectile motion represents the horizontal direction of the motion and the y-axis represents the vertical axis.

Flight of base ball, golf ball etc. are examples of projectile motion. In these cases, the projectile is projected with certain force at certain angle to vertical direction. The force that initiates motion is a contact force.

Adding vectors!

To add vectors one must follow some simple rules in order to get the answer:

1. We should always set our positive directions before starting to work on the question ( N and E)
2. To make your solution more organized, create a table for x and y components of the vectors
3. Do not forget to add the positive and negative signs. This helps in calculating the total result.
4. After putting all the values for x and y, calculate the total resultant for both the components (x and y)
5. Now you can use the resultants (x and y) to find the hypotenus of the vector and its angle by using Pythagora Theorem
6. Do not forget to write the correct units and to round off the number to the correct number of significant figures
7. Do not forget to write the directions with your final answer (North or South and East or West)

Pythagoran Theorem:

For calculating the angle:

 

 

Physics behind a roller coaster!

       Although i have "ride-phobia" and i have never even been on a merry-go-round but however all those big rides always make me wonder that what makes them work? Today we are going to discuss the king of rides- the roller coaster! Have you ever considered that what makes a roller coaster work? The answer is kinematics! Kinematics is the the study of motions. From studying kinematics we can know the acceleration, position, time taken, displacement and velocity of a certain object.

The three laws of Newton that apply to the roller coaster are:

1) "All objects will remain in a state of rest or continue to move with a constant velocity unless acted upon by an unbalanced force."

2) "The acceleration of an object depends inversely on its mass and directly on the unbalanced force applied to it."

3) "For every action force, there is an equal and opposite reaction force."

       With the help pf these three laws and kinematics one can understand the physics behind a roller coaster and can even build one.

       Another important thing behind the physics of the roller coaster is the law of conservation of energy. This law states that the energy cannot be created or destroyed. We know that energy therefore converts from one form to another. In a roller coaster, the potential energy is converted into kinetic energy and vice versa. Not only this but a roller coaster may convert and transform this energy in several different forms such as heat energy and light energy.

The picture of roller coaster given below won first place for technical merit in 2009 and was made by the students of A.Y Jackson!

Motion Activity

The red line shows our result that we got after walking hundred times on one graph.

 

Graph B

This is the first graph on which we worked on. For this graph we need to:

1. Walk 1m for 1s
2. Walk away from the motion detector at a constant speed for 2s
3. Stay for 3s at 3m
4. Walk towards the motion detector for 2s at a constant speed
5. Stay about 2m until the garph finishes

 

Graph C

 

 This was the second graph that we walked. For this graph:

1. Start at 3m walking towards the sensor at a constant speed for 3s.
2. Stop at about 1.5m for 1s.
3. Walk towards the sensor at a constant speed for 1s.
4. Stop at 0.5m for 2s.
5. Walk away from the sensor at a constant speed for 3s

 

Graph D

This was our third and the second hardest graph to walk but we are glad Mahdis- the pro finally got this one right :D! For this graph:

1. Stay at any position for 2s.
2. Walk away from the sensor at a constant speed of 0.5m/s for 3s.
3. Stay for 2s.
4. Walk towards the sensor at a constant speed of 0.5m/s till the end.

 

Graph E

 

This was our fourth graph and also the HARDEST one! I dont remember who got this one but im pretty sure we got it after atleast a million tries -_-''! For this graph:

1. Speed up at a constant rate for 4s walking away for the sensor.
2. Stop for 2s.
3. Walk towards the sensor at a constant speed for 3s.
4. Stop till the end.

 

Graph F
 



This was our fifth and one of the easiest graphs. We all tried it and all of us got the results pretty good but than this was the perfect one and we chose it! For this graph:

1. Walk away from the sensor at a constant speed for 3.5s.
2. Stop for 3.5s at 2m
3. Continue walking away from the sensor at a constant speed till the end of the graph

Graph G

 

This was our last graph and also one of the hardest ones. We spent most of the time on this graph. But we still dint get results close to the graph that was given and gave up on it. For this graph:

1. Walk away from the sensor at a constant speed of 0.3m/s for 3s.
2. Walk towards the sensor at a constant speed of 0.3m/s for about 4s.
3. Stop till the end of the graph.