M1 Mass on Pulley: Calculate ms-mk

[BrettL789123]

M1 has a mass of 5.790 kg. It is on a horizontal surface, connected by a massless string to a hook where mass M2 can be increased smoothly. The pulley has a negligible mass and no friction. When M2 = 3.092 kg it begins to accelerate downwards at a rate of 2.328 m/s2. Calculate ms-mk between M1 and the surface.

 

[tiny-tim]

Calculate ms-mk between M1 and the surface.

Hi BrettL789123!

(don't use m for mu … use u, or use µ )

Show us what you've tried, and where you're stuck, and then we'll know how to help.

 

[baba89]

To calculate the difference in mass between M1 and the surface (ms-mk), we can use the equation F=ma, where F is the net force acting on an object, m is the mass of the object, and a is the acceleration of the object.

In this scenario, the net force acting on M1 is the tension in the string, which is equal to the weight of M2. We can use the equation F=mg, where g is the acceleration due to gravity (9.8 m/s2), to find the weight of M2. Thus, F = (3.092 kg)(9.8 m/s2) = 30.3056 N.

Since we know that the acceleration of M1 is 2.328 m/s2, we can rearrange the equation F=ma to solve for the mass of M1. Thus, m = F/a = (30.3056 N)/(2.328 m/s2) = 13.032 kg.

Therefore, the difference in mass between M1 and the surface is equal to the mass of M1 (5.790 kg) minus the calculated mass of M1 (13.032 kg), which is equal to -7.242 kg.

In conclusion, the difference in mass between M1 and the surface (ms-mk) is -7.242 kg. This indicates that the surface must have a mass of 7.242 kg greater than M1 in order for M1 to accelerate downwards at a rate of 2.328 m/s2 when M2 has a mass of 3.092 kg.