Problem Statement 1:
Consider a movable rectangular water tank undergoing a simple harmonic motion on an inclined plane under the impact of water jet controlled by a centrifugal pump driven by a matlab program. So problem in front of us is to vary the discharge through nozzle such that the water tank always execute S.H.M between extremes of the shown inclined plane. As shown in the figure water jet impacts the other side of tank through a hole large enough to facilitate the entrance of water jet and water entering through the hole stays inside the tank itself.
INPUTS (To be assumed):
1. Angular frequency of oscillation of tank(say ω)
2. Dimension of tank (lXbXh), where l=length,
b=breadth, h=height up to entrance hole
3. Length of inclined plane ,say L
4. Angle of inclination(say α).
5. Cross sectional area of nozzle(say A).
6. Initial Mass of Tank(say M).
Assumptions:
1. Water jet always strikes the wall of tank perpendicularly.
2. Area of jet emerging from nozzle remain constant throughout.
3. Effect of friction can be neglected.
4. Consider simple harmonic motion to be isochronous.
5. Nozzle inclination is adjustable so that point of impact remains constant.
6. Condition of topple should not be examined.
Results required:
1. Plot the graph of Discharge through nozzle w.r.t time.
2. Total time required for filling of tank.
NOTE: appropriate data should be assumed to gain closer results.
Problem Statement 2:
Table tennis, also known as ping - pong, is a sport in which two or four players hit a lightweight, hollow ball back and forth using table tennis rackets. The game takes place on a hard table divided by a net. The challenge is to give a solution to whether a table tennis service is valid or not following the double service rules. Dimensions of a table tennis table are given below:-
DOUBLES SERVICE RULE:-
That service must originate from the right hand "box" in such a way that the first bounce of the serve bounces once in said right hand box and then must bounce at least once in the opponent side's right hand box (far left box for server), or the receiving pair score a point.
INPUTS:-
OUTPUT:-
Consider a movable rectangular water tank undergoing a simple harmonic motion on an inclined plane under the impact of water jet controlled by a centrifugal pump driven by a matlab program. So problem in front of us is to vary the discharge through nozzle such that the water tank always execute S.H.M between extremes of the shown inclined plane. As shown in the figure water jet impacts the other side of tank through a hole large enough to facilitate the entrance of water jet and water entering through the hole stays inside the tank itself.
INPUTS (To be assumed):
1. Angular frequency of oscillation of tank(say ω)
2. Dimension of tank (lXbXh), where l=length,
b=breadth, h=height up to entrance hole
3. Length of inclined plane ,say L
4. Angle of inclination(say α).
5. Cross sectional area of nozzle(say A).
6. Initial Mass of Tank(say M).
Assumptions:
1. Water jet always strikes the wall of tank perpendicularly.
2. Area of jet emerging from nozzle remain constant throughout.
3. Effect of friction can be neglected.
4. Consider simple harmonic motion to be isochronous.
5. Nozzle inclination is adjustable so that point of impact remains constant.
6. Condition of topple should not be examined.
Results required:
1. Plot the graph of Discharge through nozzle w.r.t time.
2. Total time required for filling of tank.
NOTE: appropriate data should be assumed to gain closer results.
Problem Statement 2:
Table tennis, also known as ping - pong, is a sport in which two or four players hit a lightweight, hollow ball back and forth using table tennis rackets. The game takes place on a hard table divided by a net. The challenge is to give a solution to whether a table tennis service is valid or not following the double service rules. Dimensions of a table tennis table are given below:-
DOUBLES SERVICE RULE:-
That service must originate from the right hand "box" in such a way that the first bounce of the serve bounces once in said right hand box and then must bounce at least once in the opponent side's right hand box (far left box for server), or the receiving pair score a point.
- Velocity of the racket
- Angle of service from horizontal plane(XY plane)
- Angle of service from vertical plane(XZ plane)
- Height at which the ball is hit from the table.
- X- coordinate at which the ball is hit.
- Take coefficient of restitution as 0.9 between the table surface and ball.
- Elastic collision between racket and ball.
- Neglect spinning of ball.
OUTPUT:-
- Whether the shot is valid or not.
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