Draw a free body diagram and Apply Newton's 2nd law in both direction.
60 kg chair is pulled along a rough horizontal surface under the action of a 200N force 30 degrees up from horizontal, as shown the acceleration of the chair is 1.5 m/s^2.
a) Determine the normal force on the chair.
b) Determine the frictional force acting on the chair.
c) Determine the coefficient of friction between the chair and the surface.
a. Fn = Mg-200*sin30.
b. 200*Cos30-Fk = M*a.
Fk = ?.
c. u = Fk/Fn
To solve this problem, we will first draw a free body diagram and then apply Newton's second law in both directions.
a) To determine the normal force on the chair, we need to consider the forces acting on it. The main forces acting on the chair are the weight (mg) and the normal force (N). In this case, the weight acts vertically downward and has a magnitude of (60 kg)(9.8 m/s^2) = 588 N. The normal force acts perpendicular to the surface and counteracts the weight.
The acceleration of the chair is given as 1.5 m/s^2. Since the chair is pulled at an angle of 30 degrees up from the horizontal, we need to resolve the force of 200 N into its vertical and horizontal components. The vertical component of the force is (200 N)(sin 30) = 100 N.
Now, let's draw the free body diagram of the chair:
---------------
| |
| N |
| |
| o |
| ↑ |
| mg |
| |
----------------
The forces acting on the chair are the normal force (N) and the weight (mg).
Applying Newton's second law in the vertical direction, we have:
N - mg = 0
Since the chair is not accelerating vertically, the net force in the vertical direction is zero. Therefore, the normal force is equal to the weight of the chair:
N = mg = (60 kg)(9.8 m/s^2) = 588 N
b) To determine the frictional force acting on the chair, we need to consider the forces acting horizontally. The horizontal component of the applied force is (200 N)(cos 30) = 173.2 N. The frictional force (f) opposes the motion and acts in the opposite direction to the applied force.
Applying Newton's second law in the horizontal direction, we have:
f - (173.2 N) = (60 kg)(1.5 m/s^2)
Simplifying the equation:
f = (60 kg)(1.5 m/s^2) + (173.2 N) = 263.2 N
Therefore, the frictional force acting on the chair is 263.2 N.
c) To determine the coefficient of friction between the chair and the surface, we can use the equation:
f = μN
Substituting the known values, we have:
263.2 N = μ(588 N)
Simplifying the equation:
μ = 263.2 N / 588 N = 0.447
Therefore, the coefficient of friction between the chair and the surface is approximately 0.447.