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
[86.6025- [(-50 + (100)(-9.8)](.1)]/100
[86.6025- (-48)]/100
and so I got 1.346 as the answer.
Is this correct?
The force is 120N, not 100. I should have caught that earlier. Otherwise, it looks good.
100N* cos30 -(100Nsin30+mg)(.1)= m*acceleration
To find the acceleration of the mass, let's break down the equation step by step:
1. Start with the equation:
120N * cos(30°) - (120N * sin(30°) + mg) * 0.1 = m * acceleration
2. Simplify using trigonometric identities:
120N * (0.866) - (120N * 0.5 + mg) * 0.1 = m * acceleration
3. Calculate the values inside the parentheses:
103.92N - (60N + mg) * 0.1 = m * acceleration
4. Distribute the 0.1 to the terms inside the parentheses:
103.92N - 0.1 * (60N + mg) = m * acceleration
5. Simplify further:
103.92N - 6N - 0.1mg = m * acceleration
6. Combine like terms:
97.92N - 0.1mg = m * acceleration
7. Rearrange the equation to solve for acceleration:
acceleration = (97.92N - 0.1mg) / m
8. Substitute the values given:
acceleration = (97.92 * 120 - 0.1 * 100 * 9.8) / 100
9. Calculate the result:
acceleration = (11750.4 - 98) / 100
acceleration = 11652.4 / 100
acceleration = 116.524 m/s^2
Therefore, the acceleration of the mass is approximately 116.524 m/s^2.