A 2.90 kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.320. Determine the kinetic frictional force that acts on the box for each of the following cases
a)The elevator is stationary
b) The elevator is accelerating upward with an acceleration whose magnitude is 2.20 m/s2
(c) The elevator is accelerating downward with an acceleration whose magnitude is 2.20 m/s2
Multiply the coefficient of friction by the force applied to the box by the floor. This force equals M g for part (a). In the other cases you have to take into account the acceleration of the elevator, which changes the applied force.
i'm sorry i'm confused what am i multiplying togethor and how do i solve for b and c
To determine the kinetic frictional force acting on the box in each of the three cases, we need to consider the equation for frictional force: F_friction = μ_k * N, where F_friction is the frictional force, μ_k is the coefficient of kinetic friction, and N is the normal force.
The normal force is the force exerted by the floor on the box perpendicular to the surface of contact. In each case, the normal force will vary depending on the situation.
a) The elevator is stationary:
When the elevator is stationary, the box is not experiencing any acceleration. Therefore, the normal force is equal to the weight of the box, which is given by the equation N = m * g, where m is the mass of the box and g is the acceleration due to gravity (9.8 m/s^2).
Thus, N = 2.90 kg * 9.8 m/s^2 = 28.42 N.
Now we can calculate the frictional force using the equation F_friction = μ_k * N.
So, F_friction = 0.320 * 28.42 N = 9.10 N.
b) The elevator is accelerating upward:
When the elevator is accelerating upward, there is an additional force acting on the box due to the acceleration. The normal force will be reduced because part of it is used to counterbalance the motion caused by the acceleration.
To calculate the normal force, we need to subtract the force due to the acceleration from the weight of the box. The force due to acceleration is given by the equation F_acceleration = m * a, where m is the mass of the box and a is the acceleration of the elevator.
So, F_acceleration = 2.90 kg * 2.20 m/s^2 = 6.38 N.
Now, to calculate the normal force, we subtract F_acceleration from the weight of the box: N = m * g - F_acceleration = 2.90 kg * 9.8 m/s^2 - 6.38 N = 27.74 N.
Finally, we can calculate the frictional force using the equation F_friction = μ_k * N.
So, F_friction = 0.320 * 27.74 N = 8.88 N.
c) The elevator is accelerating downward:
Similar to the previous case, when the elevator is accelerating downward, there is an additional force acting on the box. In this case, the force due to acceleration will be added to the weight of the box because it contributes to the downward force acting on the box.
Using the same equation as before, F_acceleration = m * a, we get F_acceleration = 2.90 kg * 2.20 m/s^2 = 6.38 N.
Now, to calculate the normal force, we add F_acceleration to the weight of the box: N = m * g + F_acceleration = 2.90 kg * 9.8 m/s^2 + 6.38 N = 34.06 N.
Lastly, we can determine the frictional force using the equation F_friction = μ_k * N.
Therefore, F_friction = 0.320 * 34.06 N = 10.90 N.
In summary:
a) The kinetic frictional force when the elevator is stationary is 9.10 N.
b) The kinetic frictional force when the elevator is accelerating upward is 8.88 N.
c) The kinetic frictional force when the elevator is accelerating downward is 10.90 N.