Question

8. Assuming no friction and a truly horizontal track, what is the largest acceleration the glider can
experience when being pulled by masses on the hanger? In this thought experiment, you are not
limited to just the masses we have available in lab, You must explain your answer.

Answer 1

Newton's second law allows concentrating that the response for maximum acceleration of the system is equal to the acceleration of gravity (a = g)

 

Newton's second law states that the net force is proportional to the product of the mass and the acceleration of the body  

         F = m a

The bold letters indicate vectors, F is the force, m and the mass and acceleration of the body, respectively.

The reference system is a coordinate system with respect to which measurements are made, in this case let's set a system where the x-axis is horizontal and the positive part is in the direction of movement, the y-axis is vertical.

In the attached we can see a diagram of the indicated system, as it indicates that there is no friction force, we write the equations for each part

truck

              T = Ma

Hanging masses

              T- m g = m a

for the rope to stay taut, the acceleration must be the same. We solve the system

             M a - m g = m a

             a = $\frac{m}{m+ M}$  g

This is the acceleration of the truck. Let's analyze the different cases to shrink the maximum acceleration:

• The hanging mass is much greater than the mass of the truck (m> M), we neglect the more of the truck

              a = g

• The hanging mass is less than the mass of the truck (m <M)

       a = $\frac{1}{1 + \frac{M}{m} }$ g

       a = ( $1 + \frac{M}{m}$ )⁻¹  g

The $\frac{M}{m}$ value is  much greater than the integer, we despise it the integer

      a = $\frac{m}{M}$ g

Since the truck mass is greater than the hanging mass, this acceleration is less than the acceleration of gravity.

       a <g

In conclusion, using Newton's second law we can concentrate that the response for maximum acceleration of the system is equal to the acceleration of gravity (a = g)

Learn more about Newton's second law here:

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