A small rock with mass 0.14 kg is released from rest at point A , which is at th

Question

A small rock with mass 0.14 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R = 0.56 m (the figure (Figure 1) ). Assume that the size of the rock is small compared to R, so that the rock can be treated as a particle, and assume that the rock slides rather than rolls. The work done by friction on the rock when it moves from point A to point B at the bottom of the bowl has magnitude 0.22 J.

Between points A and B, how much work is done on the rock by the normal force?

Between points A and B, how much work is done on the rock by gravity?

What is the speed of the rock as it reaches point B?

Of the three forces acting on the rock as it slides down the bowl, which (if any) are constant and which are not? Explain.

Just as the rock reaches point B, what is the normal force on it due to the bottom of the bowl?

Explanation / Answer

Between points A and B, how much work is done on the rock by the normal force?

Normal force is always perpendicular to the motion of the body, hence work done by normal force is zero as work done = force.d = Fdcos(theta) { cos(90) = 0 } so work done = 0 J

-There is no work done by the normal force because all of the work is being done by gravity.
W=0J


Between points A and B, how much work is done on the rock by gravity?
-Work done by gravity is just the gravitational potential energy lost by moving in the vertical direction, so use the equation W=mgh. In this case, h is just the radius
W=mgR
W=(.14)*(9.8)*(.56)
W=0.768 J


What is the speed of the rock as it reaches point B?
-to find the speed by using the equation W=(.5)mv^2. For this part, we have to take into account the friction, Wt=Wg-Wf. So, solving for v:
v=sqrt((Wg-Wf)/(.5*m))
v=sqrt((0.768-.22)/(.5*.14))
v=0.326 m/s


-When any object reaches the bottom of a loop or circle, the normal force is equal to the weight(mg) added to the mass times the radial acceleration(Arad). The equation looks like this: n=mg+m(Arad). First, we need to find the radial acceleration which is equal to v^2/R.
Arad=v^2/R
Arad=(0.326^2)/.56
Arad=0.189 m/s^2

Now, you just plug in everything you know:
n=mg+m(Arad)
n=(.14*9.8)+(.14*0.189)
n=1.398 N

None of the forces are constant

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