Newton's Law- 3 objects on a pulley

In summary, the three objects fall to the ground with different speeds due to the different tensions in the strings.
  • #1
johnsonandrew
88
0

Homework Statement



p4-62alt.gif


Three objects are connected by light strings as shown in Figure P4.62. The string connecting the m1 = 5.00 kg mass and the m2 = 4.00 kg mass passes over a light frictionless pulley.

a) find the acceleration of each object and
b) the tension in the two strings




Homework Equations



sumF = m*a

sumF1= m1*a = T1 - m1*g
sumF2= m2*a = T1 - m2*g - T2
sumF3= m3*a = T2 - m3*g



The Attempt at a Solution



I combined equations sumF1 and sumF2:

m1*a = T1 - m1*g
-m2*a = -T1 + m2g +T2

to get rid of one variable, T1, and I got

m2*g - m1*g + T2 = m1a - m2a

then in the sumF3 equation I solved for T2,
T2 = m3*a + m3*g

and plugged that into the above equation to get
m2*g - m1*g + (m3*a + m3*g) =m1*a - m2*a

I then plugged in my knowns to get 9.8 m/s/s, while the answer is supposed to be 1.63 m/s/s.

Can anyone please help? Where did I go wrong? I thought I understood this..
 
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  • #2
johnsonandrew said:

Homework Statement



p4-62alt.gif


Three objects are connected by light strings as shown in Figure P4.62. The string connecting the m1 = 5.00 kg mass and the m2 = 4.00 kg mass passes over a light frictionless pulley.

a) find the acceleration of each object and
b) the tension in the two strings




Homework Equations



sumF = m*a

sumF1= m1*a = T1 - m1*g
sumF2= m2*a = T1 - m2*g - T2
sumF3= m3*a = T2 - m3*g



The Attempt at a Solution



I combined equations sumF1 and sumF2:

m1*a = T1 - m1*g
-m2*a = -T1 + m2g +T2

to get rid of one variable, T1, and I got

m2*g - m1*g + T2 = m1a - m2a

then in the sumF3 equation I solved for T2,
T2 = m3*a + m3*g

and plugged that into the above equation to get
m2*g - m1*g + (m3*a + m3*g) =m1*a - m2*a

I then plugged in my knowns to get 9.8 m/s/s, while the answer is supposed to be 1.63 m/s/s.

Can anyone please help? Where did I go wrong? I thought I understood this..
you're on track, but the stuff on the left accelerates up, and the stuff on the right acceleartes with the same magnitude, except it accelerates down, You've slipped up on your plus and minus signs.
 
  • #3
Ohh. I was wondering about that. So on the right side down would be positive if I took up to be positive on the left?
 
  • #4
johnsonandrew said:
Ohh. I was wondering about that. So on the right side down would be positive if I took up to be positive on the left?
Yes, that should work.
 
  • #5
Ahhh and it did. It gave me 1.6! Thanks a lot!
 

What is Newton's Law and how does it apply to 3 objects on a pulley?

Newton's Law, also known as the Law of Motion, states that for every action, there is an equal and opposite reaction. In the case of 3 objects on a pulley, this means that the forces acting on each object are equal and opposite, causing them to move in a coordinated manner.

What are the three objects involved in Newton's Law on a pulley?

The three objects involved are the pulley, the string/rope, and the objects attached to the ends of the string/rope. The pulley is a simple machine that allows for the transfer of force and motion between the objects.

What is the difference between fixed and movable pulleys?

A fixed pulley is attached to a stationary object and only changes the direction of the force applied. A movable pulley is attached to the object being moved and multiplies the force applied, making it easier to lift heavy objects.

How does the mass of the objects affect the motion in Newton's Law on a pulley?

The mass of the objects affects the motion by determining how much force is needed to move them. The heavier the objects, the more force is needed to lift them. According to Newton's Law, the force applied to one object will be equal to the force applied to the other objects.

Can Newton's Law on a pulley be applied to real-life situations?

Yes, Newton's Law on a pulley can be applied to various real-life situations, such as elevators, cranes, and flagpoles. In all of these situations, the movement of objects is controlled by the forces acting on them, which follow the principles of Newton's Law.

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