a toy train P of mass 3kg,is connected by a string to a wagon Q of mass 2kg.Thulu fastens a cable to P and pulls it with a force of 12N at an angle of 60degrees horizontally.the train moves over a wooden floor A frictional force of 2N act between the engineP and the floor while wagon Q experiencies a frictional force of 1N. calculate the magnitude of accelaration?.calculate the magnitude of the tentionT in the string connecting P and Q?
Well, well, well! Let's break it down, shall we?
To find the magnitude of acceleration, we need to calculate the net force acting on the system. We have the applied force pulling the train, the frictional force on the train, and the frictional force on the wagon.
The net force on the train P in the horizontal direction will be the applied force minus the frictional force:
Net force on P = 12N - 2N = 10N
Similarly, the net force on the wagon Q will be the frictional force on the wagon:
Net force on Q = 1N
Since the string connecting P and Q is inextensible, the magnitude of the tension T in the string will be equal to the net force on the wagon Q (according to Newton's third law):
T = Net force on Q = 1N
Now, to find the magnitude of acceleration, we'll use Newton's second law:
Net force = mass x acceleration
For the train P:
10N = 3kg x acceleration
Therefore, the magnitude of acceleration is:
acceleration = 10N / 3kg ≈ 3.33 m/s²
So, the magnitude of acceleration is approximately 3.33 m/s² and the magnitude of the tension in the string is 1N.
Well, that was one wild trip for the train and the wagon! I hope they didn't forget their boarding passes!
To find the acceleration, we need to apply Newton's second law of motion, which states that the force applied on an object is equal to its mass multiplied by its acceleration. We also need to consider the frictional forces acting on both the train and the wagon.
1. Find the net force acting on the system:
- The force applied by Thulu on the train is 12 N at an angle of 60 degrees. We can use trigonometry to find the horizontal component of this force: F_horizontal = F_applied * cos(angle).
F_horizontal = 12 N * cos(60 degrees) = 12 N * 0.5 = 6 N.
- The frictional force acting on the train is 2 N in the opposite direction to its motion.
- The frictional force acting on the wagon is 1 N in the opposite direction to its motion.
Net force acting on the system = F_horizontal - Frictional force (train) - Frictional force (wagon).
Net force = 6 N - 2 N - 1 N = 3 N.
2. Calculate the total mass of the system:
Total mass = mass (train) + mass (wagon).
Total mass = 3 kg + 2 kg = 5 kg.
3. Apply Newton's second law to find the acceleration:
Net force = Total mass * Acceleration.
3 N = 5 kg * Acceleration.
Acceleration = 3 N / 5 kg = 0.6 m/s^2.
Therefore, the magnitude of acceleration is 0.6 m/s^2.
4. Calculate the tension in the string connecting the train and the wagon:
To find the tension in the string, we need to consider the force acting on the wagon.
Tension (T) = mass (wagon) * acceleration.
T = 2 kg * 0.6 m/s^2 = 1.2 N.
Therefore, the magnitude of tension in the string is 1.2 N.