Boxcar accelerating up incline, pendulum suspended within

[lizzyb]

This seems like an easy problem but my answer is incorrect.

Imagine a boxcar traveling up a 9.85 degree slope with constant acceleration a. In the boxcar is a pendulum that hangs 24.05 degree from the perpendicular to the boxcar's ceiling and floor. Find the acceleration.

It seems to me that the pendulum is off 14.2 degrees from vertical, and so we have:

T sin(24.05 - 9.85) = m a : Fx
T cos(24.05 - 9.85) - mg = 0 : Fy

So solving for a we have a = tan(14.2) g

Yet this is not the correct solution. Any ideas? thanx.

 

[andrevdh]

You assumed that the acceleration is in the x-direction (horizontal). Maybe the given acceleration is along the direction of the incline.

 

[kyle8921]

While your approach is correct, there may be some errors in your calculations. It is important to double check your work and make sure all units are consistent.

First, let's clarify the given information. The pendulum is hanging at an angle of 24.05 degrees from the perpendicular to the boxcar's ceiling and floor. This means that the angle between the pendulum and the slope is actually 9.85 degrees (90 - 24.05 = 65.95 degrees, which is the angle between the perpendicular and the slope, and 65.95 - 56.1 = 9.85 degrees, which is the angle between the pendulum and the slope).

Now, let's set up our equations:

Fx: T sin(9.85) = m a
Fy: T cos(9.85) - mg = 0

Solving for T in the second equation, we get T = mg/cos(9.85). Substituting this into the first equation, we get:

m g tan(9.85) = m a

Simplifying, we get a = g tan(9.85), which is the same as your solution. Therefore, it seems that the error may have been in the calculation of the angle between the pendulum and the slope. Double check your work and make sure all units are consistent (e.g. using radians instead of degrees).

It is also possible that there are other forces at play in this scenario, such as friction or air resistance, that may affect the acceleration of the boxcar and the pendulum. It is important to consider all possible factors when solving a problem like this.

In conclusion, while your approach was correct, it is important to double check your calculations and consider all possible factors that may affect the solution. Science is a continuous process of experimentation and refinement, and it is important to always strive for accuracy in our results.