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Materiale propedeutico

Materiale propedeutico

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A man moving in a straight line to the north travels 6 meters between the time t = 0 and the time t = 2 s. In the same time interval, its velocity decreases by 2 m/s.

Which of the following statements is correct?

(b) There is necessarily an instant, within the interval of time considered, in which man is stationary

(c) The average acceleration is southward

(e) The speed is always directed southwards because it slows down

(a) Its average acceleration is $1 \, \mathrm{\frac{m}{s^2}}$

(d) The final velocity is zero

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Consider a Cartesian frame of reference (x, y) in the plane. A case moves $4 \, \mathrm{m}$ along the y-axis, under the effect of a force $\vec{F} = F_x \hat{i} + F_y \hat{j}$ . If the work done by force is worth $16 \, \mathrm{J}$ , what can be said of force $\vec{F}$ ?

The work is given by the scalar product between the force $\vec F$ and the displacement $\Delta \vec{r}$

(e) $\left | \vec{F} \right | = 4 \, \mathrm{N}$

(a) che $F_y = 4 \, \mathrm{N}$

(c) che $F_x = 4 \, \mathrm{N}$

(d) Non si può dire nulla sulla forza $\vec{F}$

(b) che $F_x = 0 \, \mathrm{N}$ e $F_y = 4 \, \mathrm{N}$

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Consider carriers

$\begin{cases}{\vec{v} = 1 \hat{i}+ 1\hat{j}\\ \vec{u}=1\hat{i}- 1 \hat{j} \end{cases}$

Which of the following statements is true?

(d) The carrier $\vec{s} =\vec{v} + \vec{u}$ modulus is $|\vec{s}|=\sqrt{2}$

(a) The modulus of the carrier $\vec{d} =\vec{v} - \vec{u}$ is $|\vec{d}|=1$

(b) The modulus of the carrier $\vec{d} =\vec{v} - \vec{u}$ is $|\vec{d}|=\sqrt{2}$

(e) The modulus of the carrier $\vec{d} =\vec{v} - \vec{u}$ is $|\vec{d}|=4$

(c) The modulus of the carrier $\vec{s} =\vec{v} + \vec{u}$ is valid $|\vec{s}|=2$

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Si consideri un sistema di riferimento cartesiano (x, y) nel piano. Una cassa si sposta di $4 \, \mathrm{m}$ lungo l'asse y, sotto l'effetto di una forza $\vec F = 2 \hat{i} + 3 \hat{j} \, \mathrm{N}$ . Quanto vale il lavoro fatto dalla forza $\vec F$ ?

Il lavoro è dato dal prodotto scalare tra la forza $\vec F$ e lo spostamento $\Delta \vec{r}$

(e) $W = 12 \, \mathrm{J}$

(b) $W \simeq 21 \, \mathrm{J}$

(a) $W \simeq 28 \, \mathrm{J}$

(c) $W \simeq 40 \, \mathrm{J}$

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Si considerino due vettori nel piano, $\vec{u} = 3 \hat{i} + 3 \hat{j}$ e $\vec{v} = \frac{5\sqrt{3}}{2} \hat{i} +\frac{5}{2} \hat{j}$

. Quanto vale l'angolo tra i due vettori?

Si ricordi che il prodotto scalare $\vec{u}\cdot~\vec{v}$ si può scrivere in due modi diversi, usando i moduli o usando le componenti...

(a) $-15 ^{\circ}$

(d) $15 ^{\circ}$

(b) $75 ^{\circ}$

(c) $30 ^{\circ}$

(e) $20 ^{\circ}$

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Si consideri un sistema di riferimento cartesiano (x, y) nel piano. Una cassa si sposta di $4 \, \mathrm{m}$ lungo l'asse y, sotto l'effetto di una forza $\vec{F} = F_x \hat{i} + F_y \hat{j}$ . Se il lavoro compiuto dalla forza vale $16 \, \mathrm{J}$ , cosa si può dire della forza $\vec{F}$ ?

Il lavoro è dato dal prodotto scalare tra la forza $\vec F$ e lo spostamento $\Delta \vec{r}$

(e) $\left | \vec{F} \right | = 4 \, \mathrm{N}$

(a) che $F_y = 4 \, \mathrm{N}$

(c) che $F_x = 4 \, \mathrm{N}$

(d) Non si può dire nulla sulla forza $\vec{F}$

(b) che $F_x = 0 \, \mathrm{N}$ e $F_y = 4 \, \mathrm{N}$

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Una forza $\vec F$ di modulo pari a 10 N e la cui direzione forma un angolo di 45 gradi con quella orizzontale, è applicata ad una cassa, che si sposta orizzontalmente di 4 metri. Quanto vale il lavoro fatto dalla forza $\vec F$ ?

Il lavoro è dato dal prodotto scalare tra la forza $\vec F$ e lo spostamento $\Delta \vec r$ .

(c) $W \simeq 21 \, \mathrm{J}$

(a) $W \simeq 28 \, \mathrm{J}$

(d) $W \simeq 40 \, \mathrm{J}$

(e) $W \simeq 12 \, \mathrm{J}$

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Considera i vettori

$\begin{cases}{\vec{v} = 1 \hat{i}+ 1\hat{j}\\ \vec{u}=1\hat{i}- 1 \hat{j} \end{cases}$

Quale delle seguenti affermazioni è vera?

(a) Il modulo del vettore $\vec{d} =\vec{v} - \vec{u}$ vale $|\vec{d}|=1$

(e) Il modulo del vettore $\vec{d} =\vec{v} - \vec{u}$ vale $|\vec{d}|=4$

(c) Il modulo del vettore $\vec{s} =\vec{v} + \vec{u}$ vale $|\vec{s}|=2$

(b) Il modulo del vettore $\vec{d} =\vec{v} - \vec{u}$ vale $|\vec{d}|=\sqrt{2}$

(d) Il modulo del vettore $\vec{s} =\vec{v} + \vec{u}$ vale $|\vec{s}|=\sqrt{2}$

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The force $\vec{F}$ vector has modulus equal to $2 \, \mathrm{N}$ and is applied at the point P, which is distant $1\, \mathrm{m}$ from the pole O. Which of the following statements is correct)?

(a) $| \vec{M} | = 2 \, \mathrm{N \, m}$ and $\vec{M}$ has an inward

(e) $| \vec{M} | =0\,\mathrm{N\,m}$

(d) $| \vec{M} | = \frac{\sqrt{2}}{2} \, \mathrm{N \, m}$ and $\vec{M}$ has outgoing

(b) $| \vec{M} | = 2\sqrt{2} \, \mathrm{N \, m}$ and $\vec{M}$ has inward direction/p>

(c) $| \vec{M} | =\sqrt{2}\,\mathrm{N\,m}$ and $\vec{M}$ has an outgoing

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Consider the two vectors

$\begin{cases}\vec v = 2 \hat i + 2 \hat j \\ \vec u = - 4 \hat i - 4 \hat j \end{cases}$

Which of the following statements is true?

(e) the angle that the two vectors form is 120°

(d) the angle that the two vectors form is equal to 0

(b) the angle that the two vectors form is 45°

(c) the angle that the two vectors form is 90°

(a) the angle that the two vectors form is 180°

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