With friction turned on, set the initial velocity of the box to2.0 m/s, the coef

Question

With friction turned on, set the initial velocity of the box to2.0 m/s, the coefficient of friction to 0.55, and the mass to 0.5kg. Assume the acceleration due to gravity has a magnitude of 9.8m/s2.

(a) What is the magnitude of the frictionalforce acting on the block while it is in motion?

(b) What is the acceleration of the box? Defineto the right as the positive direction, as in the simulation.

(c) What is the distance traveled by the boxbefore coming to rest?

(d) How much time passes before the block comesto rest?

(a)

(b)

(c)

(d)

(a)

N

Explanation / Answer

The force of friction is proportional to the normal force(Since we are working on a plane then this normal force, N, isequal to the weight of the box that it W=m*g. ) where theproportionality constant is called the coefficient of friction(Note: this coeficient is different for kinetic or static systemsbut you probably know this already) . Well then a) The force due to friction is: *N=*W=0.55*0.5kg*9.8m/s^2 . The force of friction will oppose the blocks motion so it willpoint in the negative direction (since the velocity is positive).Now, Newton's 2nd Law states that F=ma so we have *N=m*a.Solving for a we get a=*g (since N=m*g) Remember thatthis will point in the negative direction so is actuall a=-*gif we take the sign of the force. . To find out how far the block gets we can use the followingequation of motion: .      V^2=Vo^2 +a*x    where V is the finalvelocity (zero in this case since we want to know how far it gotuntil it stoped) Vo is the initial velocity (given to be 2m/s)and x is the displacement (what we are looking for) .      so we have the followingequation ofmotion:       0=(2m/s)^2-*g*x    solvingfor x we get: .      x=(2m/s)^2/(*g) . To find the time we also have a simple equation ofmotion: .      V=Vo +at     (here t is the timeellapsed) with V=0, Vo=2m/s and a=-*g we thenget:   t=(2m/s)/(*g) . .

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.