If the coefficient of kinetic friction between the box and the roof is 0.50, with wha

[Sethwell]

You and your friend Peter are putting new shingles on a roof pitched at 24^\circ . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4 m away, asks you for the box of nails. Rather than carry the 2.4 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him.
- Part A
If the coefficient of kinetic friction between the box and the roof is 0.50, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

I have no idea how to get the answer to this please help
what is the answer or what eq's should i use to figure it out?

 

[Hootenanny]

Welcome to Physics Forums.

HINT: What is the acceleration of the box?

 

[nlightner]

I would approach this problem by first identifying the relevant equations and variables involved. In this case, we can use the equation for the force of kinetic friction (Ff = μkN) and the equation for the force of gravity (Fg = mg) to determine the acceleration of the box as it slides down the roof. We can also use the equation for kinematic motion (vf^2 = vi^2 + 2ad) to solve for the final velocity of the box as it reaches the edge of the roof.

To solve for the acceleration, we need to determine the normal force (N) acting on the box. This can be calculated by using the equation for the force of gravity and taking into account the angle of the roof (24 degrees). Once we have the normal force, we can plug it into the equation for the force of kinetic friction to solve for the acceleration.

Once we have the acceleration, we can then use the kinematic equation to solve for the final velocity. We know that the initial velocity (vi) is zero, as the box is initially at rest. We also know the distance the box needs to travel (5.4 m) and we can calculate the acceleration from the previous step. Solving for vf will give us the speed at which the box needs to be pushed in order to gently come to rest at the edge of the roof.

I am unable to provide the specific numerical answer without knowing the mass of the box, but this is the general approach that can be used to solve this problem. It is important to note that this solution assumes ideal conditions and does not take into account any external factors that may affect the motion of the box.