How Much Power Is Required to Accelerate a Box with Friction Involved?

[BEANTOWN]

Homework Statement

A 5.0 kg box is sliding across the floor at 2.0 m/s when it is accelerated to 8.00 m/s in 1.8 s. If the coefficient of friction is .220 how much power is required to accelerate the box?

m = 5.0 kg vi= 2.0 m/s vf = 8.00 m/s change in time = 1.8 s coefficient = .22

Homework Equations

Power = Work (W) / change in time (t)
W= Fnetd

Fnet = ma

The Attempt at a Solution

P= w/ t

w= FNetd

Heres my issue. I know Fnet(net force) = ma, which i can easily calculate. The problem is where do i use the coefficient of friction they gave me. Do I need to use it, if i already have Fnet?

 

[Matt4936]

You find the force acting against the box and take that away from the force required to accelerate the box to get the net force.

 

[BEANTOWN]

So what do i use for the w= Fnetd calculation?

 

[Matt4936]

F(net)=F(applied)-F(friction)
D= distance the box moved after acceleration

 

[asteriatic]

I would suggest approaching this problem by first identifying the key concepts and equations involved. In this case, we are dealing with work, energy, and power, as well as Newton's laws of motion. The given information includes the mass of the box, its initial and final velocities, the time it takes to accelerate, and the coefficient of friction.

To solve for the power required to accelerate the box, we can use the equation P = W/t, where W is the work done on the box and t is the time it takes to do the work. The work done on the box is equal to the change in its kinetic energy, which can be calculated using the equation KE = 1/2mv^2. Note that we can use the initial and final velocities to find the change in kinetic energy, as well as the mass of the box.

Now, to find the work done on the box, we need to consider the forces acting on it. The only external force acting on the box is the force of friction, which is given by the coefficient of friction multiplied by the normal force (mg) of the box. This frictional force acts in the opposite direction of motion, so it will do negative work on the box. Therefore, we can write the work done on the box as W = -Ff*d, where d is the distance the box travels while accelerating.

To find the distance d, we can use the equation vf^2 = vi^2 + 2ad, where a is the acceleration of the box. Rearranging this equation, we get d = (vf^2 - vi^2)/2a. Now, we can substitute this expression for d into our work equation and solve for W.

Finally, we can plug in the calculated W and the given t into the power equation to find the power required to accelerate the box. Remember to use the appropriate units for each quantity in the equations.

In summary, to solve this problem, we need to use the equations for kinetic energy, work, and power, as well as the equation for finding the distance traveled by an object with constant acceleration. We also need to consider the forces acting on the box, including the frictional force, and use the given information to find the necessary quantities.