Dynamics 6. Start a new problem in 1. (35 points) The mass of box is 15 kg with

Question

Dynamics 6. Start a new problem in 1. (35 points) The mass of box is 15 kg with the static friction coefficient 0.15 and 0.1 for kinetic friction coefficient on the surface is at rest and about to be released. (a) Prove that this is a Dynamics problem using friction forces. (b) Find the new static friction coefficient to hold the box at the current position if you can change the static friction coefficient by having a different surface material for the surface. (c) Find the new angle in deg. that will keep the box static with the static friction coefficient 0.2. (d) Find the acceleration of the box. (e) Find the velocity of the box at 10 seconds. (f) Find the velocity when it moves 2 m from the origin. (g) Find the time when the box is at 2 m from the origin.

Explanation / Answer

A. Component of weight along slope = m * g * Sin(30) = 15 * 9.81 * 1/2 = 73.58 N

Static Frictional Force = 0.15 * m * g * Cos(30) = 19.12 N

Since, Component of weight along slope > Static Frictional Force

So, This is dynamics problem

B. Component of weight along slope = m * g * Sin(30) = 15 * 9.81 * 1/2 = 73.58 N

So, for holding the box at current position:

Component of weight along slope = us *  m * g * Cos(30)

us *  m * g * Cos(30) = 73.58

us = 0.58 <---------------ans

C. Component of weight along slope = m * g * Sin(Thita)

So, for holding the box at current position:

Component of weight along slope = Static Friction

15 * 9.81 * Sin(thita) = 0.2 * 15 * 9.81 * Cos(thita)

Tan(thita) = 0.2

Thita = 11.31 degree <---------------------ans

D. Fnet = Component of weight along slope - Static friction

m * a = Component of weight along slope - Static friction

m*a = 73.58 - 19.12

a = 3.631 m/s2 <-----------ans

E. V = U + at

U = 0

V = at

V = 3.631 * 10 = 36.31 m/s <-------------------ans

F. V2 - U2 = 2 a *S

V2 = 2 * 3.631 * 2

V = 3.81 m/s <-------------------ans

E.

S = Ut + 1/2 a * t2

2 = 0 + 1/2 * 3.631 * t2

t = 1.05 sec <-------------ans

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