Question

Give one experimental setup that can show the principle of the law of acceleration. Explain as to why is it able to illustrate the law.

Answer 1

The experimental set-up consists of a glider on an air track connected by a string passing over a small pulley to a hanging load of mass m and weight mg. We consider the glider and the load as a single object, subject to the accelerating force mg. To show that the acceleration of the system is proportional to the acceleration force when the total mass is kept constant, we begin with a hanging load of mass m and add four identical metallic discs of mass m to the glider of mass M (Fig. 1) Therefore, the accelerating force mg acts on a system of total mass M + 5m. To double the accelerating force, one disc is transferred from the glider to the hanging load. To triple the force, two discs are transferred from the glider to the hanging load, and so on [4]. To show that the acceleration of the system is inversely proportional to its mass when the accelerating force is kept constant, we change the mass of the system by loading the glider with mass of different sizes or connecting another glider to

The original.

  

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Figura 1 - A simplified drawing of the air track showing the hanging load and the glider loaded with metallic discs.

The acceleration can be determined from the average speeds calculated for successive time intervals of the motion. For a question of availability and cost, we have measured time intervals by using electronic counters in conjunction with a single-crystal oscillator circuit operating at 1 kHz and a photogate [5]. The timing circuit is shown in Fig. 2.

Figure 2 - The timing circuit.

The counters have two inputs: the clock (CK) and the clock enable (CL EN). The first receives the rectangular pulses sent by the oscillator and the other enables the counting process when it is held at ground state. When the logic state at this input is high, the counting stops. The heart of the circuit is the 4017. The 4017 is a decade counter with ten outputs that go to HIGH (H) in sequence when a source of pulses is connected to the clock input and when suitable logic levels are applied to the reset and enable inputs [6,7].

Briefly, the electronic circuit (Fig. 2) works as follows. If the logic state at the S0 output is initially H, the S1, S2, ... S5 outputs are LOW (L) and the state at each CL EN input is H due to the presence of the NOT gate. Consequently, all counters are blocked because an H level on the CL EN input inhibits the clock's operation. When the clock's input of the 4017 receives the first pulse, the high state is transferred from S0 to S1 and the first counter starts the timing. When the second pulse arrives, the state at S1changes from H to L and S2 goes to H. Then, the first counter stops the timing and the second starts. Finally, when the sixth pulse arrives, S5 goes from H to L and the fifth counter stops the timing, while S0 goes to H again (shining LED) because the S6 output is connected directly to reset input.

The pulses that arrive at the clock's input of the 4017 are generated during the passage of posts transported by the glider through a photogate. The glider carries six posts, evenly spaced on a wooden ruler fixed to it (Fig. 3).

Figura 3 - A simplified drawing of the glider carrying six evenly spaced posts.

So, after the posts have passed through the photogate, the counters record, in ms, the time intervals t1, t2, ... t5 indicated in Fig 3. If the distance between successive posts is d, the average speed of the glider in the time interval t1 is , in t2 is , etc. The set of these values may provide information regarding the motion of the glider.