Practice 7H: | 1 | 2 | 3 | 4 | Go up

** Force that maintains circular motion**

**1. A girl sits in a tire that is attached to an overhanging tree limb by
a rope 2.10 m in length. The girl's father pushes her with a tangential speed of 2.50 m/s. If the magnitude of the force that maintains her circular
motion is 88.0 N, what is the girl's mass?**

Here's what you know, r = 2.1 m , and v_{t}^{}
= 2.5 m/s, and
F = 88.0 N

Use the formula F_{c} = mv_{t}^{2}/r

1. Plug-in the values to
the equation and get 88 N = m * (2.5

m/s)^2 / 2.1 m

2. Solve for m and you
get m = 29.568 kg

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**2. A bicyclist is riding at a tangential speed of 13.2 m/s around a
circular track with a radius of 40.0 m. if the magnitude of the force that maintains the bike's circular motion is 377 N, what is the combined mass of the
bicycle and rider?**

Here's what you know, r = 40 m , and F = 377 N, and v_{t}^{}
=
13.2 m/s.

Use the formula F_{c} = mv_{t}^{2}/r

1. Plug-in the values to
the equation and get 377 N = m *

((13.2 m/s)^2 / 40.0 m)

2. Solve for m and get m
= 86.5 kg

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**3. A dog sits 1.5 m from the center of a merry-go-round with an angular
speed of 1.2 rad/s. If the magnitude of the force that maintains the dog's circular motion is 40.0 N, what is the dog's mass?**

Here's what you know, r = 1.5 m , and w
= 1.20 rad/s
and F = 40 N.

Use the formula F_{c} = mv_{t}^{2}/r and w
= v_{t }/ r

1. First find v with the
formula w
= v_{t }/ r rewriting it as w*r=v_{t }

2. Plug in the values and
get 1.2 rad/s * 1.5 m = 1.8 m/s

3. Use the velocity just
calculated and plug it into the

formula F = m* v_{t}^{2}/r rewritten as F / (v_{t}^{2}/r)=m

4. Solve for m and get m
= 18.5 kg

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**4. A 905 kg test car travels around a 3.25 km circular track. if the
magnitude of the force that maintains the car's circular motion is 2140 N, what is
the car's tangential speed?**

Here's what you know, circumference = 3250 m , and F =
2140 N, and

m = 905 kg. Use the formula = v_{t }/ r and circumference =
2pr
and

also

F_{c} = mv_{t}^{2}/r

1. First find the radius
by using the circumference formula

2 Solve that to get
r = 517.25 m

2. Next use F_{c}
= mv_{t}^{2}/r to find the tangential velocity. F = 2140
N, r = 517.25 m, m = 905 kg

3. Plug in the values to
get v = 34.97 m/s = 35 m/s

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