Question

question 7 1 pts a cart with a trapezoidal shape, as in the figure, carries a blue box of unknown mass on its slanted, flat surface. the surface makes an angle of 15° with the horizontal. the box is not sliding up or down relative to the slanted surface, staying always at the same height. the free - body diagram for the blue box is shown on the right of the figure. (vec{n}) is the normal force, and (vec{f}_g) is gravity. there are no other forces acting on the blue box. what is the acceleration of the cart? if needed, use (g = 9.81space m/s^2).
options:
2.54 (m/s^2)
2.63 (m/s^2)
9.48 (m/s^2)
0 (m/s^2)
4.90 (m/s^2)

Explanation:

Step1: Define coordinate system

Align x-axis parallel to the slanted surface, y-axis perpendicular to it.

Step2: Resolve gravity force

Gravitational force component along x-axis: $F_{Gx} = mg\sin(15^\circ)$

Step3: Apply Newton's second law

$\sum F_x = ma = mg\sin(15^\circ)$, mass $m$ cancels out: $a = g\sin(15^\circ)$

Step4: Calculate acceleration

Substitute $g=9.81\ \text{m/s}^2$, $\sin(15^\circ)\approx0.2588$:
$a = 9.81 \times 0.2588 \approx 2.54\ \text{m/s}^2$

Answer:

2.54 m/s²