My Math Forum Need help - Newton's second law of motion

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 May 16th, 2017, 10:52 PM #1 Newbie   Joined: May 2017 From: Davao Posts: 5 Thanks: 0 Need help - Newton's second law of motion A 2.0 ton elevator is supported by a cable that can safely support 6400 lb. What is the shortest distance in which the elevator can be brought to a stop when it is descending with a speed of 4.0 ft/s? A 2.0 ton elevator is supported by a cable that can safely support 6400 lb. What is the shortest distance in which the elevator can be brought to a stop when it is descending with a speed of 4.0 ft/s? A 50-kg block is placed on a smooth horizontal surface. A horizontal chord attached to the block passes over a light frictionless pulley and is attached to a 4.0-kg body. Find the acceleration and the tension in the chord when the system is released. Two bodies having the masses m1=30g and m2=40g are attached to the ends of a string of negligible mass and suspended from a light frictionless pulley. Find the accelerations of the bodies and the tension in the string.
 May 17th, 2017, 03:51 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,549 Thanks: 1259 Well, you posted the first problem twice, so I suppose it's important to start there. Maximum upward net force would be $6400 - 4000 = 2400 \, lbs$. Using $g= 32 \, ft/s^2$ ... $a_{max}=\dfrac{F_{net}}{m}=\dfrac{2400}{125} = 19.2 \, ft/s^2$ You may now use the kinematics equation, $v_f^2 = v_0^2 + 2a \Delta x$, to determine the minimum displacement required to bring the elevator to a stop. For the second problem, I assume you've sketched a diagram. Net force on the table mass is just tension ... $T = Ma$ Net force on the hanging mass is its weight minus the same tension ... $mg - T = ma$ Solve the system of equations for acceleration, $a$, then determine the tension, $T$. Atwood machine problem ... net force on each mass again. $m_2 g - T = m_2 a$ $T - m_1 g = m_1 a$ summing the two equations eliminates $T$ ... $m_2 g - m_1 g = m_2 a + m_1 a$ You may now solve for the magnitude of acceleration, $a$, then go back and determine the value of tension, $T$.
 May 17th, 2017, 04:24 AM #3 Newbie   Joined: May 2017 From: Davao Posts: 5 Thanks: 0 Thank you so much. Great help!
 May 17th, 2017, 04:36 AM #4 Newbie   Joined: May 2017 From: Davao Posts: 5 Thanks: 0 Where did you get the 6400-4000=2400 lbs?
May 17th, 2017, 05:32 AM   #5
Math Team

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see attached force diagram ... like the one you made, correct?
Attached Images
 Fnet.jpg (20.9 KB, 5 views)

 May 17th, 2017, 07:00 AM #6 Newbie   Joined: May 2017 From: Davao Posts: 5 Thanks: 0 Thanks! How about this problem? Find the torque created by a 10-N force acting 60°N of E at a distance of 1m from the axis of rotation of a lever.
May 17th, 2017, 07:16 AM   #7
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Quote:
 Originally Posted by Camsybel Thanks! How about this problem? Find the torque created by a 10-N force acting 60°N of E at a distance of 1m from the axis of rotation of a lever.
$\tau = \vec{r} \times \vec{F} = |\vec{r}| \, |\vec{F}| \, \sin{\theta}$

you have been given the magnitude & direction for $\vec{F}$, but only the magnitude of $\vec{r}$ ... what is the direction of $\vec{r}$? Is there a diagram given?

 May 17th, 2017, 07:34 AM #8 Newbie   Joined: May 2017 From: Davao Posts: 5 Thanks: 0 There is no diagram given.
May 17th, 2017, 07:53 AM   #9
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Quote:
 Originally Posted by Camsybel There is no diagram given.
I hate to assume ... maybe the statement infers that $\theta = 60^\circ$

Use the torque formula I provided in my previous post.

Poorly worded question, imho.

 Tags law, motion, newton

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