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?
Net force= mass*acceleration
Horizontal force -frictionalforce = mass*acceleration
100N* cos30 -(100sin30+mg)(.1)= m*acceleration
check that.
When you write "mass*acceleration" do you mean the acceleration of the mass?
100N* cos30 -(100sin30+mg)(.1)= m*acceleration
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?
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?
Yes, the equation "mass*acceleration" means the acceleration of the mass. So in this case, it refers to the acceleration of the 100 kg mass.
To calculate the acceleration, you correctly used the equation:
Net force = mass * acceleration
Where the net force is the horizontal force minus the frictional force.
In this scenario, the horizontal force is: 100 N * cos(30°)
The frictional force is: (100 sin(30°) + mg) * coefficient of sliding friction
Since the mass is 100 kg and the acceleration is what we're trying to find, we can rewrite the equation as:
100 N * cos(30°) - (100 sin(30°) + 100 kg * 9.8 m/s^2) * 0.1 = 100 kg * acceleration
Now, calculating the values:
Horizontal force = 100 N * cos(30°) = 86.602 N
Frictional force = (100 sin(30°) + 100 kg * 9.8 m/s^2) * 0.1 = 123.305 N
Net force = 86.602 N - 123.305 N = -36.703 N (negative because it opposes the motion)
Finally, solving for acceleration:
-36.703 N = 100 kg * acceleration
acceleration = -36.703 N / 100 kg
acceleration ≈ -0.367 m/s^2
So, the acceleration of the 100 kg mass is approximately -0.367 m/s^2.