a box is being pushed at a constant velocity. The coefficient of kinetic friction between the box and the surface is 0.3 . At one point in the journey the coefficient of kinetic friction between the box and the surface suddenly jumps to 0.55. if the force of the push does not change, what is the acceleration of the box after change in friction?
At the beginning, the box is in uniform rectilinear motion (URM), which means that the horizontal force is just enough to balance the frictional resistance, where
Pushing force, F
=Frictional resistance = μkmg
= 0.3 mg
With increase in coefficient of friction,
the net force on the box is now
F=(0.3-0.5)mg=-0.2mg
Acceleration = F/m=-0.2g
i.e. decelerting
To find the acceleration of the box after the change in friction, we need to consider the net force acting on the box.
Before the change in friction, the box is being pushed at a constant velocity, which means that the force of the push is equal to the force of kinetic friction opposing it.
Let's denote the force of the push as Fp and the force of the kinetic friction as Ff.
Before the change in friction:
Fp = Ff
After the change in friction, the force of kinetic friction increases to a higher value. Let's denote the new force of kinetic friction as Ff_new.
The equation for the net force acting on the box is given by:
Net force = Fp - Ff
After the change in friction:
Net force = Fp - Ff_new
We know that the force of the push (Fp) remains the same, so the net force is different. Considering Newton's second law of motion, which states that F = m * a (force equals mass times acceleration), we can rearrange the equation to solve for acceleration:
Acceleration = Net force / mass
To determine the acceleration, we need the mass of the box. If the mass is not provided, we won't be able to determine the acceleration precisely.
To find the acceleration of the box after the change in friction, we need to consider the forces acting on the box.
Before the change in friction, the box is being pushed with a constant velocity. This means that the force of the push is equal and opposite to the force of kinetic friction. The formula for kinetic friction is:
F_friction = μ_k * F_normal,
where F_friction is the force of friction, μ_k is the coefficient of kinetic friction, and F_normal is the normal force exerted on the box by the surface.
Since the box is moving at a constant velocity, we know that the force of the push is equal to the force of kinetic friction:
F_push = F_friction.
Now, after the change in friction, the coefficient of kinetic friction suddenly jumps to 0.55. The force of the push remains the same. Let's assume the force of the push is denoted by F_push, the acceleration of the box is denoted by a, and the mass of the box is denoted by m.
The net force acting on an object can be calculated using Newton's second law of motion:
F_net = m * a,
where F_net is the net force acting on the box.
To find the net force after the change in friction, we need to consider the forces acting on the box. These forces are the force of push (F_push) and the force of kinetic friction (F_friction) with the new coefficient of kinetic friction (0.55):
F_net = F_push - F_friction(new).
Since we already know that F_push is equal to F_friction (before the change in friction), we can substitute F_friction with F_push:
F_net = F_push - F_push(new).
Now we can substitute the formula for kinetic friction and rearrange the equation:
F_net = μ_k * F_normal - μ_k(new) * F_normal.
We can see that the normal force (F_normal) cancels out, so:
F_net = μ_k - μ_k(new) * F_normal.
Since we're given the masses, we can substitute F_net with m * a:
m * a = μ_k - μ_k(new) * F_normal.
Now we need to solve for the acceleration (a):
a = (μ_k - μ_k(new)) * F_normal / m.
However, we are not given the value of the normal force (F_normal) or the mass (m) of the box. To find the acceleration, we would need to know either the normal force or the mass.