On a mass of 100 kg, a force of 120 N acts right and at an angle of 30 degrees to the horizontal. If the coefficient of sliding friction is .1 what is the acceleration of the mass?
100N* cos30 -(100sin30+mg)(.1)= m*acceleration
does "m*acceleration mean the acceleration of the mass?"
15.425- [(-98.803 + (100)(-9.8)](.1)
15.425- (-1078.803)(.1)
and so I got 123.305 as the answer.
I also did the math in radians mode. Is this correct?
m is mass, * means multiply.
this comes from net force= mass*acceleration
The calculations are nonsense: The angles were given in degrees, sin30 means the sin of thirty degrees, not the sin of thirty radians. Redo the calcs in degrees.SIDS
The equation you provided, which is net force = mass * acceleration, is the correct formula to use to solve this problem. However, there seems to be some confusion in the calculations you have shown.
To correctly calculate the acceleration of the mass, we need to break down the forces acting on it. The force acting to the right and at an angle of 30 degrees to the horizontal can be resolved into its horizontal and vertical components.
The horizontal component of the force is given by 120 N * cos(30 degrees) = 103.92 N.
The vertical component of the force is given by 120 N * sin(30 degrees) = 60 N.
The gravitational force acting on the mass is given by the product of its mass (100 kg) and the acceleration due to gravity (-9.8 m/s^2), which gives us a value of -980 N.
The sliding friction force is given by the coefficient of sliding friction (0.1) multiplied by the sum of the vertical component of the force and the gravitational force, which gives us -0.1(60 N - 980 N) = -98 N.
Now, we can calculate the net force acting on the mass:
Net force = Horizontal force - Friction force
= 103.92 N - (-98 N)
= 201.92 N
Finally, we can use the formula net force = mass * acceleration to find the acceleration:
201.92 N = 100 kg * acceleration
Dividing both sides of the equation by 100 kg gives us:
acceleration = 201.92 N / 100 kg = 2.0192 m/s^2
So, the correct value for the acceleration of the mass is 2.0192 m/s^2.
Regarding your question about using radians mode, it is not necessary in this case since the given angles are in degrees. The trigonometric functions sin() and cos() will automatically use degrees as the default unit if no unit is specified.