Finding the acceleration of a crane trolley and it's load.

In summary, the problem involves an object of weight 8526 N hanging at an angle of 5.0° as the crane's trolley at point P moves to the right with constant acceleration. The acceleration of the trolley and load can be calculated using the equation 9.8 / tan (90-5) = 0.857 m/s^2. The intuition behind this problem is that gravity does not directly affect the horizontal acceleration, but since the trolley is increasing its altitude, some work must be done against gravity. This can be solved using Newton's second law, F = ma, and taking components in a convenient direction.
  • #1
Dylan.Wallett
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Homework Statement


An object of weight 8526 N hangs at an angle of 5.0° when the crane’s trolley at point P moves to the right with constant acceleration, as shown in the diagram.
Calculate the acceleration of the trolley and load.


Homework Equations


9.8 / tan (90-5) = 0.857 m/s^2


The Attempt at a Solution


I am looking for the intuition to the problem.
I have worked out that because there is no resistance in the equation so that the weight of the load does not effect horizontal acceleration only the work done to get the trolley up to acceleration magnitude.

I would like to know intuitively why gravity effects the horizontal acceleration of the trolley. I would appreciate your help.
 
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  • #2
Welcome to PF!

Hi Dylan! Welcome to PF! :smile:

As is usual in dynamics questions, you only need to use good ol' Newton's second law F = ma …

draw a free body diagram and take components in a convenient direction :wink:​
 
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Likes Irfan Nafi
  • #3
gravity does not affect horizontal acceleration (except through friction, which we are ignoring) but the acceleration is not completely horizontal. since the trolley is increasing its altitude (i assume, you do not indicate whether moving to the right is going up or down) some work must be done against gravity.
 

Related to Finding the acceleration of a crane trolley and it's load.

1. How do you calculate the acceleration of a crane trolley and its load?

To calculate the acceleration of a crane trolley and its load, you will need to measure the initial velocity and final velocity of the trolley and its load, as well as the time it takes for the trolley to change its velocity. Then, use the formula: acceleration = (final velocity - initial velocity) / time.

2. What units are used to measure acceleration?

The standard units for acceleration are meters per second squared (m/s²) or feet per second squared (ft/s²).

3. How does the mass of the load affect the acceleration of the crane trolley?

The mass of the load does affect the acceleration of the crane trolley. The larger the mass of the load, the more force is needed to move it, resulting in a slower acceleration. Conversely, a lighter load will require less force and result in a faster acceleration.

4. What other factors can affect the acceleration of a crane trolley and its load?

In addition to mass, other factors that can affect the acceleration of a crane trolley and its load include the friction between the trolley and the track, air resistance, and the angle of the track. These factors can either increase or decrease the acceleration depending on their magnitude.

5. How can the acceleration of a crane trolley and its load be measured?

The acceleration of a crane trolley and its load can be measured using various methods such as using motion sensors, accelerometers, or calculating the acceleration from velocity and time data. It is important to ensure that the measurements are accurate and taken consistently to get an accurate result.

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