In Figure 10-53, two blocks, of mass m1 =400 g and m2 =600 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 500 g and radius R = 12.0 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest.
(a) Find the magnitude of the acceleration of the blocks.
m/s2
(b) Find the tension T1 in the cord at the left.
N
(c) Find the tension T2 in the cord at the right.
N
First, calculate the moment of inertia for the pulley.
Then, notice on the pulley that angular acceleration is related to cord acceleration by
alpha*radius= linear acceleration.
Now, writing a system equation...
m2*(g-a)= pulling force by gravity
I*alpha= Torque on pulley
I*alpha/radius = force on pulley extreme
I*acceleration/radius^2
m1*a= tension on m1
or
m2*(g-a)=I*a /r^2+m1*a
solve for a.
check my thinking.
i need help with writing system of equations for ages
To write a system of equations for this problem, you will need to consider the forces acting on each block and the pulley. For the blocks, you will need to consider the force of gravity and the tension in the cord. For the pulley, you will need to consider the torque due to the tension in the cord.
For the block on the left, the equation would be:
m1*a = T1 - m1*g
For the block on the right, the equation would be:
m2*a = T2 - m2*g
For the pulley, the equation would be:
I*alpha = T1*R - T2*R
Where I is the moment of inertia of the pulley, alpha is the angular acceleration, T1 and T2 are the tensions in the cord, and R is the radius of the pulley.
Once you have written the equations, you can solve them simultaneously to find the acceleration, tension in the cord, and angular acceleration of the pulley.
To write a system of equations for ages, you need to know specific information about the ages of the individuals involved. Let's consider an example to demonstrate how to write these equations.
Suppose you have three people: Alice, Bob, and Carol. Let's denote their ages by A, B, and C, respectively. Here are a few scenarios and how you can represent them as a system of equations:
1. Alice is twice as old as Bob, and Carol is 5 years younger than Alice.
- A = 2B (Alice is twice as old as Bob)
- C = A - 5 (Carol is 5 years younger than Alice)
2. The sum of their ages is 80, and Carol is 10 years older than Bob.
- A + B + C = 80 (The sum of their ages is 80)
- C = B + 10 (Carol is 10 years older than Bob)
3. Alice is 3 years older than Bob, and Carol is 4 years younger than Bob.
- A = B + 3 (Alice is 3 years older than Bob)
- C = B - 4 (Carol is 4 years younger than Bob)
These examples demonstrate how you can represent different relationships between ages as a system of equations. You can add or modify equations depending on the specific information given about the ages in the problem.