Pulley Tension Problem

In summary, the problem involves two masses connected by a light pulley system, and the question asks for the relation between their accelerations, tensions in the strings, and the accelerations in terms of the masses and gravity. The solution involves using free-body diagrams and considering the effects of friction and contact forces between the pulleys and cables. It is important to note that the acceleration of pulley 1 and mass m2 will be the same, but the acceleration of mass m1 may be different.
  • #1
yitriana
36
0
Problem is written, a diagram of the problem is attached.

Homework Statement


An object of mass m1 on a frictionless horizontal table is
connected to an object of mass m2 through a very light pulley
P1 and a light fixed pulley P2 as shown in Figure P5.34.
(a) If a1 and a2 are the accelerations of m1 and m2, respectively,
what is the relation between these accelerations? Express
(b) the tensions in the strings and (c) the accelerations
a1 and a2 in terms of the masses m1 and m2, and g.

Homework Equations





The Attempt at a Solution



I am confused on how to approach the problem since I don't understand how the pulley 1 affects pulley 2.
 

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  • #2
Pulley 1 affects Pulley 2 through tension in the cable between them and contact force of the cable laying across Pulley 2. This contact force leads to friction between the cable and Pulley 2. However, if the contact between the cable and Pulley 2 is frictionless, then the only effect of Pulley 1 on Pulley 2 is the contact force, which you probably simply assume to be balanced by the pivot force.

Bottomline: I don't think that you really want to know how Pulley 1 affects Pulley 2, and, assuming zero friction, this will not help you solve the problem.
 
  • #3
I'm sure you know this already, but you've got to use free-body diagrams to figure this one out. In this case, you'll need 3: one for each of the masses and one for pulley 1. The one hint I'll give you is that, since pulley 1 and M2 are connected by a string, they have to have the same acceleration. That doesn't mean M1 has the same acceleration, though.
 

What is a pulley tension problem?

A pulley tension problem is a type of physics problem that involves calculating the tension force in ropes or cables that are attached to a system of pulleys. This type of problem is commonly used to demonstrate the principles of mechanical advantage and the distribution of forces.

How do you calculate the tension in a pulley system?

The tension in a pulley system can be calculated by using the equation T = (m1 + m2)g, where T is the tension force, m1 is the mass of the first object, m2 is the mass of the second object, and g is the acceleration due to gravity. This equation assumes that the pulley and ropes are massless and there is no friction involved.

What factors affect the tension in a pulley system?

The tension in a pulley system can be affected by several factors, including the mass of the objects being lifted, the number of pulleys in the system, and the angle at which the ropes are attached to the pulleys. Friction in the pulleys and ropes can also affect the tension.

How can you increase the tension in a pulley system?

To increase the tension in a pulley system, you can either increase the mass of the objects being lifted or decrease the number of pulleys in the system. Additionally, decreasing the angle at which the ropes are attached to the pulleys can also increase the tension.

What is the difference between static and dynamic tension in a pulley system?

Static tension refers to the tension force in a pulley system when all the objects are stationary. Dynamic tension, on the other hand, refers to the tension force when the objects in the system are in motion. The dynamic tension is usually greater than the static tension due to the added force of acceleration.

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