A train is moving along a straight horizontal track. A pendulum suspended from the roof of one of the carriages of train is inclined at four degree to the vertical. Calculate tge acceleration of train
Le A be the angle of inclination (4 degrees).
T = string tension force.
Write the vertical and horizontal Newton's second law equations
W = M g = T cos A
M a = T sin A
Eliminate T
a/g = tan A = 0.0699
Solve for a
mg=TcosA
ma=TsinA
a/g=sinA/cosA
a/g=tanA
=0.0699
a=g*0.0699=9.81*0.0699= 0.6857m/s^2
To calculate the acceleration of the train, we can use the concept of a pendulum.
The angle of inclination of the pendulum can tell us about the acceleration of the train.
Given:
Angle of inclination (θ) = 4 degrees
Formula:
Acceleration (a) = g * tan(θ)
Where:
g = acceleration due to gravity = 9.8 m/s^2 (approximately)
Substituting the values into the formula:
a = 9.8 m/s^2 * tan(4°)
To calculate the acceleration, we need to convert the angle from degrees to radians since the tangent function uses radians instead of degrees. We can use the formula:
radians = degrees * π / 180
Converting the angle to radians:
θ = 4° * π / 180 ≈ 0.07 radians
Now we can calculate the acceleration:
a ≈ 9.8 m/s^2 * tan(0.07 radians)
Using a calculator, we can find:
a ≈ 9.8 m/s^2 * 0.001247 ≈ 0.0122 m/s^2
Therefore, the acceleration of the train is approximately 0.0122 m/s^2.
To calculate the acceleration of the train, we can use the concept of apparent weight.
When the train is moving with a constant velocity along a straight horizontal track, the pendulum will appear to be inclined due to the acceleration acting on the train. This apparent inclination can be related to the acceleration of the train using trigonometry principles.
Let's break down the steps to find the acceleration of the train:
Step 1: Measure the actual inclination angle of the pendulum.
In this case, the actual inclination angle of the pendulum is given as 4 degrees.
Step 2: Calculate the apparent inclination angle.
The apparent inclination angle can be calculated by considering the relationship between the actual and apparent angles. Since the train is moving horizontally, the apparent inclination angle is equal to the actual inclination angle. Therefore, the apparent inclination angle is also 4 degrees.
Step 3: Apply trigonometry.
The apparent weight of the pendulum can be determined by resolving the gravitational force acting on it into vertical and horizontal components. The horizontal component can be related to the apparent inclination angle using trigonometry.
In this case, the vertical component of the gravitational force is equal to the weight of the pendulum, and the horizontal component is equal to the force causing the pendulum to appear inclined, which is the acceleration (a) of the train.
Using trigonometry, we can write:
sin(apparent angle) = horizontal component / weight of the pendulum
sin(4 degrees) = a / weight of the pendulum
Step 4: Solve for the acceleration of the train.
Rearranging the equation, we can isolate the acceleration (a) of the train:
a = sin(4 degrees) * weight of the pendulum
Note: To further calculate the acceleration, we would need additional information, such as the weight of the pendulum or any other relevant details.