A 3.70kg box is sliding across the horizontal floor of an elevator.
The coefficient of kinetic friction between the box and the floor is 0.470.
Determine the kinetic frictional force that acts on the box when
(a) The elevator is stationary.
(b) The elevator is accelerating upward with an acceleration whose magnitude is 2.90 m/s2.
(c) The elevator is accelerating downward with an acceleration whose magnitude is 2.90 m/s2
Wb = 3.70 kg * 9.8 N./kg = 36.3 N. =
Weight of box.
Fb = 36.3 N. @ 0 Deg. = Force of box.
Fp = 36.3*sin(0) = 0. = Force Parallel
to floor.
Fv = 36.3*cos(0) = 36.3 N. = Force perpendicular to floor.
a. Fk = u*Fv = 0.470 * 36.3 = 17.1 N.=
Force of kinetidc friction.
To determine the kinetic frictional force acting on the box in different scenarios, we need to use the formula:
Frictional Force = Coefficient of Kinetic Friction * Normal Force
The normal force is the force exerted by the floor on the box and is equal to the weight of the box when the elevator is stationary. However, when the elevator is accelerating, the normal force changes because of the presence of an additional force due to the acceleration.
(a) When the elevator is stationary:
The normal force is equal to the weight of the box, which is given by the equation: Weight = mass * acceleration due to gravity
Weight = 3.70 kg * 9.8 m/s^2 = 36.26 N
The kinetic frictional force is then: Frictional Force = 0.470 * 36.26 N = 17.04 N
Therefore, the kinetic frictional force acting on the box when the elevator is stationary is 17.04 N.
(b) When the elevator is accelerating upward:
In this case, the normal force is the sum of the weight of the box and the additional force due to the upward acceleration.
Weight = 3.70 kg * 9.8 m/s^2 = 36.26 N
Additional force = mass * acceleration = 3.70 kg * 2.90 m/s^2 = 10.73 N
The normal force is then: Normal Force = Weight + Additional force = 36.26 N + 10.73 N = 46.99 N
The kinetic frictional force is: Frictional Force = 0.470 * 46.99 N = 22.10 N
Therefore, the kinetic frictional force acting on the box when the elevator is accelerating upward with an acceleration of 2.90 m/s^2 is 22.10 N.
(c) When the elevator is accelerating downward:
Similar to the previous case, the normal force is the sum of the weight of the box and the additional force due to the downward acceleration. However, in this case, the additional force is subtracted from the weight.
Weight = 3.70 kg * 9.8 m/s^2 = 36.26 N
Additional force = mass * acceleration = 3.70 kg * 2.90 m/s^2 = 10.73 N
The normal force is then: Normal Force = Weight - Additional force = 36.26 N - 10.73 N = 25.53 N
The kinetic frictional force is: Frictional Force = 0.470 * 25.53 N = 12.00 N
Therefore, the kinetic frictional force acting on the box when the elevator is accelerating downward with an acceleration of 2.90 m/s^2 is 12.00 N.