Inclined plane problem

In summary, we have a 1-meter inclined board with a height of 0.3 meters and a block with a mass of 122.5g connected to a string and a pulley. When a weight of 50g is hung from the pulley, the block moves with constant velocity. The ideal mechanical advantage is 2450, the actual mechanical advantage is 0.45, and the theoretical efficiency is 0.4176. The input force is 122.5g, the input work is 2.7735J, and the output work is 0.7177J. The experimental AMA is 2.45 and the experimental efficiency is 0.2588.
  • #1
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Homework Statement



a 1meter board is inclined at 10 degrees with a height of .3 meters. a block with mass of 122.5g is placed at the bottom connected to a string which is connected to a pulley at the top. if a weight of 50g is hung from the pulley and the block moves with constant velocity, what is the ideal and actual mechanical advantage(theoretical), predicted efficiency(theoretical), input force(tension), input work, output work, AMA(experimental), and efficiency(experimental).


Homework Equations





The Attempt at a Solution

 
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  • #2
Ideal mechanical advantage= output force/input force=122.5g/.05g=2450Actual mechanical advantage= net output force/input force=22.5g/50g=0.45Theoretical efficiency= output work/input work=122.5g*9.8m/s^2*sin10°*.3m/50g*9.8m/s^2=.4176Input force=MA*input force=2450*.05g=122.5gInput work=input force*distance=122.5g*9.8m/s^2*sin10°*.3m=2.7735JOutput work=output force*distance=50g*9.8m/s^2*sin10°*.3m=.7177JAMA(experimental)= output force/input force=122.5g/50g=2.45Efficiency(experimental)= output work/input work=.7177J/2.7735J=.2588
 
  • #3


I would approach this problem by first identifying the given information and the unknowns. From the homework statement, we are given the dimensions and mass of the inclined plane, as well as the mass and weight of the block and pulley system. The unknowns are the ideal and actual mechanical advantage, predicted efficiency, input force, input work, output work, AMA, and efficiency.

To solve for these unknowns, we can use the equations for mechanical advantage, efficiency, and work. The ideal mechanical advantage (IMA) is the ratio of the length of the incline to the height, in this case 1/.3 = 3.33. The actual mechanical advantage (AMA) is the ratio of the output force to the input force, which can be calculated by considering the forces acting on the block (weight of the block, weight of the hanging weight, and tension in the string). The predicted efficiency can be calculated using the formula for efficiency, which is output work divided by input work. The input force can be found by considering the tension in the string, and the input work can be calculated by multiplying the input force by the distance the block moves. Similarly, the output work can be found by multiplying the output force (weight of the hanging weight) by the distance it moves.

To determine the AMA and efficiency experimentally, we can conduct a controlled experiment by setting up the inclined plane, block, pulley, and weights as described in the problem. We can measure the distance the block moves and the hanging weight moves, as well as the weights of the block and hanging weight. From these measurements, we can calculate the AMA and efficiency using the same equations as before.

In conclusion, by using the given information and the equations for mechanical advantage, efficiency, and work, we can determine the theoretical and experimental values for the unknowns in this inclined plane problem. Conducting an experiment to verify our calculations would provide a more accurate and reliable result.
 

1. What is an inclined plane problem?

An inclined plane problem is a type of physics problem that involves a block or object sliding or rolling down an inclined surface. The goal is to calculate the acceleration, velocity, or displacement of the object based on the given information.

2. What are the key concepts involved in solving an inclined plane problem?

The key concepts involved in solving an inclined plane problem are friction, gravity, and the relationship between force, mass, and acceleration (Newton's Second Law). It is also important to understand trigonometry and how to break forces into components along the incline and perpendicular to the incline.

3. How do you calculate the acceleration of an object on an inclined plane?

The acceleration of an object on an inclined plane can be calculated using the formula a = g * sinθ, where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of the incline. This assumes that there is no friction present.

4. How does the angle of the incline affect the acceleration of an object?

The angle of the incline affects the acceleration of an object by changing the magnitude of the component of gravity that acts along the incline. As the angle increases, the component of gravity acting down the incline decreases, resulting in a smaller acceleration. At a 90-degree angle, there is no component of gravity acting along the incline and therefore no acceleration.

5. Can an object on an inclined plane ever have a negative acceleration?

Yes, an object on an inclined plane can have a negative acceleration if the angle of the incline is greater than 90 degrees (i.e. pointing downward). In this case, the component of gravity acting along the incline is in the opposite direction of the motion, resulting in a negative acceleration.

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