Section 7H

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_t²/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_t²/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_t²/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_t²/r rewritten as F / (v_t²/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_t²/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_t²/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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