Solving a Frictionless Pulley Problem: Find m2's Acceleration

In summary, the conversation is about a physics problem involving two blocks connected by a string and a frictionless pulley. The goal is to find the upward acceleration of one of the blocks. The individual forces and equations are discussed, and it is concluded that there are three equations and four variables. However, by rearranging the equations, the desired solution can be found.
  • #1
zhenyazh
56
0
hi
can some one please help me with this for an exam?

A 33.5 kg block (m1) is on a horizontal surface, connected to a 7.10 kg block (m2) by a massless string. The frictionless pulley has a radius R = 0.081 m and a moment of inertia I=0.110 kgm2.
A force F = 244.9 N acts on m1 at an angle θ = 29.3°. There is no friction between m1 and the surface. What is the upward acceleration of m2?
an image is attached

i wrote force equation for both masses.
none of the are in equilibrium so each has its acceleration.
i also wrote one equation for the torque on the pulley. summing
all torques and equaling to I*alfa.

problem is i have too many variables. t1 t2 a1 a2 and not enough equations.
i got to be missing something.
even if i unite t1 and t2 into one variable of t1-t2,
and decide that alfa is the square root of squares of a1 and a2
i am left with one equation and two variables.

can anyone explain if i am wrong or what am i missing
or give a detailed outline of solution?

thanks
 

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  • #2
You can write three equations.
F*cosθ - T1 = m1*a ...(1)
T1 - T2 = I*α...(2)
T2 - m2*g = m2*a...(1)
Now solve for a.
 
  • #3
thanks. it worked
 

FAQ: Solving a Frictionless Pulley Problem: Find m2's Acceleration

How do I determine the acceleration of m2 in a frictionless pulley problem?

The acceleration of m2 in a frictionless pulley problem can be determined using the equation a = F/m, where a is the acceleration, F is the net force acting on the object, and m is the mass of the object. In a frictionless pulley system, the net force on m2 is equal to the tension in the string attached to the pulley. Therefore, the acceleration of m2 can be calculated by dividing the tension by the mass of m2.

What is the role of the frictionless pulley in this problem?

The frictionless pulley serves as a point of support for the string and allows for the transfer of tension between the two masses. It also ensures that there is no friction present, which simplifies the problem and allows for a more accurate calculation of the acceleration of m2.

Can the acceleration of m2 be negative in this problem?

Yes, the acceleration of m2 can be negative in a frictionless pulley problem. This would occur if the mass m2 is moving in the opposite direction of the applied force, resulting in a negative net force and negative acceleration. It is important to pay attention to the direction of motion and forces when solving these types of problems.

How does the mass of m1 affect the acceleration of m2 in a frictionless pulley problem?

The mass of m1 does not directly affect the acceleration of m2 in a frictionless pulley problem. However, the mass of m1 does affect the tension in the string, which in turn affects the acceleration of m2. The larger the mass of m1, the greater the tension in the string and the greater the acceleration of m2 will be.

Is the acceleration of m2 constant in a frictionless pulley problem?

Yes, the acceleration of m2 is constant in a frictionless pulley problem. This is due to the fact that there is no friction present, so there are no external forces acting on the object that would cause its acceleration to change. As long as the system remains frictionless, the acceleration of m2 will remain constant throughout its motion.

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