Question

question 1 (1 point)
a 40 - kg crate attached to a rope is being lowered with a downward acceleration of 2.0 m/s². what is the magnitude of the force exerted by the rope on the crate?
a) 400 n
b) 200 n
c) 520 n
d) 470 n
e) 310 n

Explanation:

Step1: Identify forces acting on crate

The force of gravity $F_g = mg$ acts down - ward and the tension force $T$ exerted by the rope acts upward. Let the downward direction be positive. According to Newton's second - law $F_{net}=ma$. So, $F_g - T=ma$.

Step2: Calculate the force of gravity

The mass of the crate $m = 40$ kg and the acceleration due to gravity $g = 9.8$ m/s². Then $F_g=mg=40\times9.8 = 392$ N.

Step3: Rearrange the Newton's second - law equation for tension

From $F_g - T=ma$, we can solve for $T$. Rearranging gives $T=F_g - ma$.

Step4: Substitute values to find tension

We know $m = 40$ kg, $a = 2.0$ m/s², and $F_g=392$ N. Then $T=392-40\times2=392 - 80=312\approx310$ N.

Answer:

E. 310 N