Question
A tugboat is pushing two barges (labeled 1 and 2) so that they speed up. The masses of the tugboats and barges and the accelerations of the systems are given for each case. Ignore the effects of fluid friction.
Rank the magnitude of the force the tugboat exerts on barge one.
▶️Answer/Explanation
Ans:
\( \begin{aligned} F_A & =\left(m_{n e t}\right) \cdot a_{n e t} \\ & =(80 m+15 m+25 m) 1.2 \\ & =120 m \times 1.2 \\ & =144 \times 100 \\ F_A & =14400 \mathrm{~N}\end{aligned} \)
\( \begin{aligned} F_B & =\left(m_{n e t}\right) \cdot a_{n e t} \\ & =(70 m+15 m+25 m) 1.2 \\ & =110 m \times 1.2 \\ & =132 \times 100 \\ F_B & =13200 \mathrm{~N}\end{aligned} \)
\( \begin{aligned} F_C & =\left(m_{n e t}\right) \cdot a_{n e t} \\ & =(60 m+15 m+25 m) 1.5 \\ & =110 m \times 1.2 \\ & =150 \times 100 \\ F_C & =15000 \mathrm{~N}\end{aligned} \)
\( \begin{aligned} F_D & =\left(m_{n e t}\right) \cdot a_{n e t} \\ & =(60 m+20 m+20 m) 1.0 \\ & =100 m \times 1.2 \\ & =100 \times 100 \\ F_D & =10000 \mathrm{~N}\end{aligned} \)
Rank: \( F_C>F_A>F_B>F_D \)
Question(a)-(c)
A small box is on a ramp tilted at an angle above the horizontal. The box may be subject to the following forces: frictional (ƒ), gravitational (mg), pulling or pushing \((F_p)\) and normal (N). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces.
Question(a)
Which figure best represents the free-body diagram for the box if it is accelerating up the ramp?
(A) Figure A
(B) Figure B
(C) Figure C
(D) Figure D
(E) Figure E
Answer/Explanation
Question(b)
Which figure best represents the free-body diagram for the box if it is at rest on the ramp?
(A) Figure A
(B) Figure B
(C) Figure C
(D) Figure D
(E) Figure E
Answer/Explanation
Question(c)
Which figure best represents the free-body diagram for the box if it is sliding down the ramp at constant speed?
(A) Figure A
(B) Figure B
(C) Figure C
(D) Figure D
(E) Figure E