A 14.0-kg chair is at rest on a flat floor. The coefficient of static friction between
the chair and the floor is 0.450. A person tries to move the chair by pushing on the
chair with a force directed at an angle of 30„a below the horizontal. What is the
minimum force that the person must apply in order to move the chair?
Wc = m*g = 14kg * 9.8N/kg = 137.2 N. =
Wt. of chair.
Fc = 137.2 N. @ 0o = Force of chair.
Fp = 137.2*sin(0) = 0 = Force Parallel
with floor.
Fv=137.2*cos(0) + Fap*sin(-30)
Fv=137.2 - 0.5Fap. =Force perpendicular to floor. = Normal.
Fn = Fap*cos(-30)-Fp-Fs = m*a.
Fap-0-0.45(137.2-0.5Fap) = m*0 = 0
Fap-61.74+0.225Fap = 0
0.775Fap-61.74 = 0
0.775Fap = 61.74
Fap = 79.7 N @ (-30o).
To find the minimum force that the person must apply in order to move the chair, we need to consider the forces acting on the chair.
The force that the person is applying can be resolved into two components: one component perpendicular to the floor and one component parallel to the floor.
The component perpendicular to the floor does not affect the motion of the chair since it is perpendicular to the force of gravity. Therefore, we only need to consider the component parallel to the floor.
Let's denote the force of gravity acting on the chair as F_g, the normal force between the chair and the floor as N, and the force of friction between the chair and the floor as F_friction.
The force of gravity acting on the chair can be calculated using the formula F_g = m*g, where m is the mass of the chair and g is the acceleration due to gravity.
F_g = 14.0 kg * 9.8 m/s^2 = 137.2 N
The normal force N is equal in magnitude and opposite in direction to the force of gravity acting on the chair. Therefore, N = -137.2 N.
The force of friction F_friction can be calculated using the formula F_friction = μ*N, where μ is the coefficient of static friction.
F_friction = 0.450 * 137.2 N = 61.74 N
Now, we need to find the minimum force that the person must apply in order to overcome the force of friction.
Since the chair is at rest, the force applied by the person must be equal in magnitude and opposite in direction to the force of friction.
Therefore, the minimum force that the person must apply is 61.74 N.
Note: The angle of 30 degrees below the horizontal is irrelevant in this calculation because we only need to consider the horizontal component of the applied force.