The coefficients of static and kinetic friction between a 476 N crate and the ware house floor are 0.615 abd 0.420, repectively. A worker gradually increases his horizontal push against this crate utnil it just begins to move and from them on maintains that same maximum push. What is the acceleration of the crate after it has begun to move?

Question

The coefficients of static and kinetic friction between a 476 N crate and the ware house floor are 0.615 abd 0.420, repectively. A worker gradually increases his horizontal push against this crate utnil it just begins to move and from them on maintains that same maximum push. What is the acceleration of the crate after it has begun to move?

Answer 1

Netforce=ma

mg(mus-muk)=ma
solve for a

Answer 2

To determine the acceleration of the crate after it has begun to move, we need to understand the forces acting on the crate. There are two types of friction to consider: static friction and kinetic friction.

To begin with, the worker gradually increases their horizontal push against the crate until it just begins to move. At this point, the force applied by the worker is equal to the maximum static friction, which can be calculated as:

F_static = µ_s * N

Where:
F_static is the maximum static friction
µ_s is the coefficient of static friction
N is the normal force acting on the crate

The normal force (N) is equal to the weight of the crate (mg), where m is the mass of the crate and g is the acceleration due to gravity. In this case, we are given the weight of the crate, which is 476 N.

Next, we need to calculate the kinetic friction force. Once the crate starts moving, the force of kinetic friction is given by:

F_kinetic = µ_k * N

Where:
F_kinetic is the force of kinetic friction
µ_k is the coefficient of kinetic friction
N is the normal force

Now that we have the maximum static friction and the force of kinetic friction, we can determine the acceleration of the crate. The net force acting on the crate is the difference between the force applied by the worker and the force of kinetic friction:

Net Force = F_applied - F_kinetic

Using Newton's second law of motion:

Net Force = mass * acceleration

We can rearrange the equation to solve for acceleration:

acceleration = (F_applied - F_kinetic) / mass

Plugging in the values:

acceleration = (F_static - F_kinetic) / mass

acceleration = (µ_s * N - µ_k * N) / mass

Now we have all the necessary information to calculate the acceleration of the crate.