A 25 kg box is set on a flat surface with us=0.62 and uk=0.49. A force of 100N is applied to the box through a rope which makes and angle of 30 degrees with the horizon.
(a)what's the component of Fa that is attempting to move the box sideways?
(b) what's the normal force on the box?
(c)what is the maximum static friction?
(d)what is the kinetic friction?
(e) Does the box move?
-if yes, what is its acceleration?
-if no. what is the static friction on the box?
(a)what's the component of Fa that is attempting to move the box sideways?
(b) what's the normal force on the box? 100cos30
(c)what is the maximum static friction?*25*9.8-100sin30)us
(d)what is the kinetic friction?
same, use uk
(e) Does the box move?
-if yes, what is its acceleration?
net force=m*a
100cos30-(25*9.8-100sin30)uk =ma
solve for a
To answer these questions, we need to apply the relevant equations and principles related to forces and friction. Let's go through each question step-by-step:
(a) What's the component of Fa that is attempting to move the box sideways?
To determine the component of the applied force (Fa) that is attempting to move the box sideways, we need to find the horizontal component of the force. This can be done by using trigonometry.
Horizontal component = Fa * cos(angle)
Horizontal component = 100 N * cos(30 degrees)
Horizontal component = 100 N * 0.866 ≈ 86.6 N
So, the component of Fa that is attempting to move the box sideways is approximately 86.6 N.
(b) What's the normal force on the box?
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the box is placed on a flat surface, so the normal force would be equal to the weight of the box.
Normal force = Weight = mass * gravity
Normal force = 25 kg * 9.8 m/s^2
Normal force ≈ 245 N
Therefore, the normal force on the box is approximately 245 N.
(c) What is the maximum static friction?
The maximum static friction can be calculated using the formula:
Fstatic friction = static friction coefficient * normal force
Given that us (the static friction coefficient) is 0.62 and the normal force is approximately 245 N, we can calculate the maximum static friction as follows:
Maximum static friction = 0.62 * 245 N
Maximum static friction ≈ 151.9 N
Therefore, the maximum static friction is approximately 151.9 N.
(d) What is the kinetic friction?
The kinetic friction is the frictional force between two objects when they are in relative motion. The formula to calculate kinetic friction is:
Fkinetic friction = kinetic friction coefficient * normal force
Given that uk (the kinetic friction coefficient) is 0.49 and the normal force is approximately 245 N, we can calculate the kinetic friction as follows:
Kinetic friction = 0.49 * 245 N
Kinetic friction ≈ 120.1 N
Therefore, the kinetic friction is approximately 120.1 N.
(e) Does the box move?
To determine whether the box will move or not, we need to compare the maximum static friction with the horizontal component of the applied force.
If the horizontal component of the applied force is greater than the maximum static friction, the box will start moving. If it is less than or equal to the maximum static friction, the box will remain stationary.
Horizontal component of applied force = 86.6 N
Maximum static friction = 151.9 N
Since the horizontal component of the applied force (86.6 N) is less than the maximum static friction (151.9 N), the box will not move. Hence, we need to find the static friction on the box.
If a box is not moving, the static friction is equal to the horizontal component of the applied force.
So, the static friction on the box is approximately 86.6 N.