Mechanics ( one easy Questionw hich i cant solve ) A-Levels Sylabbus

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SUMMARY

The discussion focuses on a mechanics problem involving a particle P on an inclined plane and a particle Q connected by a string. The problem requires proving that particle P remains stationary under specific conditions and calculating the acceleration of both particles when Q descends. The derived acceleration for Q is 5g/13 (approximately 3.846 m/s²), and the tension forces acting on both particles are expressed as T(Q) = 1.387√h and T(P) = 0.3396√h. The conclusion confirms that Q will hit the floor again before P comes to instantaneous rest.

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  • Understanding of Newton's laws of motion
  • Knowledge of forces acting on inclined planes
  • Familiarity with kinematic equations
  • Concept of tension in strings and its relation to mass and acceleration
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  • Study the principles of forces on inclined planes in detail
  • Learn about kinematic equations and their applications in mechanics
  • Explore the concept of tension in connected systems
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1 a) A particle P of mass m is placed on a rough plane inclined at an angle tan-1 (5/12) to the horizontal.The coefficient of friction between the plane and P is 0.5. Prove that P will remain stationary.

1b ) A light inextensible string is fastened to P, passes up a line of greatest slope, over a frictionless pulley at the top of the plane, and to its other end is attached a particle Q of mass 2m , which hangs freely. Prove that the particles will move and find magnitude of their acceleration.

1c ) When Q has decended a distance h , it hits the floor and rebounds with 0.5 of its speed. Show that Q will hit the floor again before P comes to instantaneous rest.

I can't solve the problem of 1C ) Someone pleae help.
No diagram is included in the question orginally.
Answers for
6b) a= 5g/13 = 3.846 ms-2
6c) T(Q) = 1.387(h)^0.5 Means Root h
T(P)=0.3396(h)^0.5 = 1.074(h/g)^0.5
So t(Q) < t(P)

PLEASE HELP!
 
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The forces acting on Q are gravity and the tension force from being connected to that other mass (and is directed opposite to the gravitational force). The sum of those two forces is equal to the mass of Q (2m) times the acceleration. Solve for the acceleration. Knowing the acceleration and the height that Q falls you can find the speed at which it hits the ground.

The problem then tells you that it rebounds at one half that speed. Find the height that it will reboud to and the time it will take to get there (the mass P should not affect this since it is not pulling on Q). Then find the time it will take to fall from that rebound height (it will be the same time that it took to rebound to that height).

At some point you got to find the time it takes for P to stop moving. To do this you calculate the time it will take for the fricional force plus the gravitational force (remembering it is on an inclined plane) to stop it from a velocity equal the velocity of Q right before it hit the ground for the FIRST time.

Longest answer ever.
 
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