Particles 1 and 2, each of mass m, are attached to the ends of a rigid massless rod of length L1 + L2, with L1 = 19 cm and L2 = 75 cm. The rod is held horizontally on the fulcrum and then released. What is the magnitude of the initial acceleration of particle 1? What is the magnitude of the initial acceleration of particle 2?
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I = mL^2, L=L1+L2
I am not given mass and the answer needs to be numerical.
Tnet=I * alpha
How do I find the initial acceleration?
F=ma o---^---------o
Assume m=1kg
F=9.8N for both
T=9.8*r T1=9.8(.19) T2=9.8(.75)
Sum T=9.8(.75-.19)=Ttotal
Ttotal=I(alpha)
I=sum(mr^2) = r1^2+r2^2
alpha=Ttotal/I
a=alpha*r a1=alpha*(.19) a2=alpha*(.75)
To find the initial acceleration of particle 1, you can use the concept of torques. The torque acting on particle 1 will cause it to rotate initially, resulting in an angular acceleration. This angular acceleration can be related to the linear acceleration of particle 1 using the moment of inertia and the equation Tnet = I * alpha.
1. Calculate the moment of inertia of the system:
The moment of inertia of the system is given by I = m * L^2, where m is the mass of each particle and L is the total length of the rod.
First, calculate L by adding the lengths L1 and L2: L = L1 + L2.
Then, substitute the given values and calculate the value of I.
2. Calculate the net torque on the system:
The net torque acting on the system is due to the weight of particles 1 and 2. The torque due to the weight is given by T = r * F, where r is the distance from the fulcrum and F is the gravitational force acting on each particle (m * g).
3. Equate the net torque to I * alpha:
Since torque is equal to I * alpha, set the torque equal to I * alpha and solve for alpha.
4. Relate angular acceleration to linear acceleration:
The linear acceleration of particle 1 is related to the angular acceleration by the equation a = alpha * r, where r is the distance from the fulcrum to particle 1.
Once you obtain the angular acceleration (alpha), you can calculate the linear acceleration (a) of particle 1 by substituting the values of alpha and the distance r into the equation.
Repeat the process above to find the initial acceleration of particle 2.