COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Question
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Chapter 6, Problem 92P

(a)

To determine

The speed of the car that has to reach the top of the loop.

(a)

Expert Solution
Check Mark

Answer to Problem 92P

The speed of the car that has to reach the top of the loop is 19.8m/s_.

Explanation of Solution

At the top of the ramp the car has only the potential energy given by

  TE=mgh        (I)

Here, m is the mass, g is the acceleration due to gravity

At the top of the circular loop the car has both kinetic and potential energy which is given by,

    TE=mgh+12mv2        (II)

Here, v is the velocity, TE is the total energy.

Equating equation (I) and (II), and solve for v.

    mgh+12mv2=mgh2gh+v2=2ghv=2g(hh)        (III)

Conclusion:

Substitute 20m for h and 40m for h in equation (III) to find v,

    v=2(9.8m/s2)(40m20m)=19.8m/s

Therefore, the speed of the car that has to reach the top of the loop is 19.8m/s_.

(b)

To determine

The force exerted at the top of the loop.

(b)

Expert Solution
Check Mark

Answer to Problem 92P

The force exerted at the top of the loop is 29051.152N_.

Explanation of Solution

Write the expression for the force exerted at the top of the loop.

    F=mv2rmg        (IV)

here, r is the radius, v is the speed.

From the above diagram it is shown that

  r=h2=20m2=10m.

Conclusion:

Substitute 10m for r, 988kg for m and 19.8m/s for v, 9.80m/s2 for g in equation (I) to find F.

    F=(988kg)(19.8m/s)210m(988kg)(9.80m/s2)=29051.152N

Therefore, The force exerted at the top of the loop is 29051.152N_.

(c)

To determine

The minimum height above the bottom of the loop.

(c)

Expert Solution
Check Mark

Answer to Problem 92P

The minimum height above the bottom of the loop is 25m_.

Explanation of Solution

The force exerted on the car by the track at the top should be equal to the weight of the car so that,

    mv2r=mgv2=rg        (V)

Using equation (I), the energy of the car at the top will be,

    E=mgh+12mv2E=mgh+12m(gr)=mgh+12mg(h2)=54mgh        (VI)

The minimum height from which the car starts is H,

According to the conservation of energy,

    mgH=54mgh        (VII)

Solve equation (VII) for H,

    H=54h        (VIII)

Conclusion:

Substitute 20m for h in equation (VIII) to find H.

    H=54(20m)=25m

Therefore, The minimum height above the bottom of the loop is 25m_.

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Chapter 6 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

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