1 – One stone is thrown from the top of a building (as we can see in the picture below), falling 15 meters after the building, after 5 seconds. We also know that 3 seconds after the throwing, the stone is at the same level of the throwing platform. Treating this stone as a pontual object, calculate:
- a) the velocity components at the instance of the throwing;
- b) the heigh (h) of the building;
- c) the average velocity vector since the throwing till the impact in the ground, and its module. Chose your own reference to use.
2 – In the image below there are two boxes, A and B (12 kg and 80 kg mass respectively) and A is pushed with an intensity force of F=70 N. Between the ground and the boxes exists friction with static coeficient of 0,30 and an unknown kinematic coeficient, but equal for both boxes. Under the action of the force F, the set has a module accelereation of 2,4 m^2/s^2. Treat the boxes as pontual objects.
- a) Mark all the forces that act in the two boxes with a free object diagram;
- b) Calculate the kinematic coeficient of the friction between the boxes and the ground, and calculate the module of the contact force between A and B;
- c) If the force N decrease intensity to 40 N, wish will be the acceleration of the system?
3 – In a flipper machine, a ball is thrown to the game by a spring, compressed and then droped, that comunicates to the ball the necessary impulse to climb into a tilted runner to the top of the game table, where it goes down to iniciate the game. The ball’s mass weights 80 gr and the table’s tilt has 7,5 degrees. The runner has a lengh of 1,9 meters (measured between the ball’s jumping platform and its top has shown in the following picture. The spring has an elastic constant of 72 N/m. We also know that the regular kinematic coeficient of friction between the runner and the ball is of 0,015.
- a) Calculate the impulse module that the ball receives from the spring to a compression of 6,0 cm. Consider the weigh contribution and the friction in the ball throwing approximately nule;
- b) Verify that the above compression is not sufficient to iniciate the game;
- c) Calculate the minimum necessary compression to iniciate the game.
4 – A washing machine drum decreases gradually and evenly its velocity till the 900 rpm till it stops, after 20,0 seconds. Calculate:
- a) Angular acceleration of the drum;
- b) The number of rotations that the drum describes till it stops.