A measurement that has both magnitude and direction

1 answer:

7 0

<span>A measurement that both magnitude and direction is a vector quantity. An example of this is a moving car. The car exerts force due to its thrust and weight that runs in it. This will give us the magnitude of the car. The resulting motion of the car in terms of displacement, velocity and acceleration that determines its direction makes it a vector quantity. On the other hand, a measurement that has only magnitude is a scalar quantity. The energy exerted by the engine of the car is a scalar quantity.</span>

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A(n) 55.5 g ball is dropped from a height of 53.6 cm above a spring of negligible mass. The ball compresses the spring to a maxi

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The spring force constant is $k=243\ \frac{N}{m}$ .

Explanation:

We are told the mass of the ball is $m=0.0555\ kg$ , the height above the spring where the ball is dropped is $h=0.536\ m$ , the length the ball compresses the spring is $d=0.04897\ m$ and the acceleration of gravity is $9.8\ \frac{m}{s^{2}}$ .

We will consider the initial moment to be when the ball is dropped and the final moment to be when the ball stops, compressing the spring. We supose that there is no friction so the initial mechanical energy $E_{mi}$ is equal to the final mechanical energy $E_{mf}$ :

$E_{mf}=E_{mi}$

Initially there is only gravitational potential energy because the force of the spring isn't present and the speed is zero. In the final moment there is only elastic potential energy because the height is zero and the ball has stopped. So we have that:

$\frac{1}{2}kd^{2}=mgh$