A block of mass M1 = 15 kg is lying on a horizontal friction-less surface is connected to a
string passing over a friction-less pulley. A mass of M2 = 25 kg is hanging at its other end as
shown in the figure below.
(i) Find the acceleration in the masses.
(ii) What is the tension in the cord that connects the two masses?
(iii) How far will m2 fall in time 2s after the system is released?
system force= 25*9.8
system mass=40kg
Force=mass*acceleration.
Tension= massbeingmoved*a=15*a
distance=1/2 a t^2
To find the answers to these questions, we can use Newton's second law and some basic principles of mechanics. Let's break down each question and explain the steps to solve them.
(i) Find the acceleration in the masses:
1. Draw a free body diagram for each mass:
- For M1: The only force acting on M1 is the tension in the string pulling it upwards.
- For M2: The force of gravity is acting downwards, and the tension in the string is acting upwards.
2. Apply Newton's second law to each mass:
- For M1: The net force acting on M1 is equal to the tension in the string. Therefore, Tension = M1 * acceleration.
- For M2: The net force acting on M2 is the difference between its weight (M2 * g) and the tension in the string. Therefore, M2 * g - Tension = M2 * acceleration.
3. Set up an equation using the above relations:
- M1 * acceleration = Tension
- M2 * g - Tension = M2 * acceleration
4. Solve the above system of equations:
- Substitute the value of Tension from the first equation into the second equation.
- Solve for acceleration.
(ii) What is the tension in the cord that connects the two masses:
- The tension in the string is the same throughout its length (assuming an ideal, massless, and frictionless string).
- Using the result from part (i), substitute the value of acceleration into Tension = M1 * acceleration.
(iii) How far will m2 fall in time 2s after the system is released:
- Use the kinematic equation s = ut + (1/2)at^2, where s is the distance, u is the initial velocity (which is 0), a is the acceleration (from part (i)), and t is the time (2s in this case).
- Plug in the values and solve for s.
By following these steps, you can find the answers to all three questions.