Three blocks of masses 1.0, 2.0, and 4.0 kilograms are connected by massless strings, one of which passes over a frictionless pulley of negligible mass, as shown above. Calculate each of the following.
a. The acceleration of the 4 kilogram block
b. The tension in the string supporting the 4 kilogram block
c. The tension in the string connected to the l kilogram block
This is an atwood's machine were on the left side there is the 2.0 kg block and the 1.0 kg block
on the right side is the 4.0 kg block
can you tell me if my answers are correct
a 2.5 m/s^2
b 39 N
Thanks
No. The net accelelerating force is (4-1-2)g
acceleration= netforce/total mass= g/(7)
How did you get double that in a)?
b)tension= 4(g-acceleration in a)
c) I am not certain where the 1 kg block is. If it is on the bottom of the left side, tension= 1g+accelearation in a)
acceleration = 1.4 m/s/s
tension of 4kg block is= 33.6 N
tension of 1kg block is= 11.2 N
To solve this problem, we can use the principles of Newton's second law and the concepts of equilibrium for the system.
First, let's analyze the forces acting on each block:
1.0 kg block:
- The tension force applied by the string going to the right.
- The weight force acting downwards (mass x acceleration due to gravity).
2.0 kg block:
- The tension force applied by the string going to the right.
- The weight force acting downwards.
4.0 kg block:
- The tension force applied by the string going to the left.
- The weight force acting downwards.
Now, let's solve for each part:
a. The acceleration of the 4.0 kg block:
To find the acceleration, we need to calculate the net force acting on the system and divide it by the total mass. In this case, since the system is in equilibrium, the net force equals zero. Therefore, the acceleration will also be zero.
b. The tension in the string supporting the 4.0 kg block:
Since the 4.0 kg block is not accelerating, the tension in the string supporting it should be equal to its weight. So, we can calculate it using the formula: tension = mass x acceleration due to gravity.
Tension = 4.0 kg x 9.8 m/s^2 = 39.2 N (rounded to 39 N)
c. The tension in the string connected to the 1.0 kg block:
To find the tension in the string connected to the 1.0 kg block, we need to calculate the net force acting on it. The net force is the difference between the weight force and the tension force acting in the opposite direction. Since the 1.0 kg block is accelerating, we can use Newton's second law to find the net force:
Net force = mass x acceleration.
mass x acceleration = 1.0 kg x 2.5 m/s^2 = 2.5 N
Since the net force equals the difference between the weight force and the tension force:
Tension - weight force = 2.5 N
The weight force is given by:
Weight force = mass x acceleration due to gravity
= 1.0 kg x 9.8 m/s^2 = 9.8 N
Therefore:
Tension - 9.8 N = 2.5 N
Tension = 2.5 N + 9.8 N = 12.3 N (rounded to 12 N)
So, your answers are:
a. The acceleration of the 4.0 kg block is 0 m/s^2.
b. The tension in the string supporting the 4.0 kg block is 39 N.
c. The tension in the string connected to the 1.0 kg block is 12 N.