3. A car initially traveling V eastward turns north by traveling in a circular path at uniform speed as shown in Figure P6.3. The length of the arc ABC is 235 m, and the 35.0 car completes the turn in 36.0 s. (a) What is the acceleration when the car is at B located at an angle of 35.0? Express your Figure P6.3 answer in terms of the unit vectors i and j. Determine (b) the car's average speed and (c) its average acceleration during the 36.0-s interval.

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3. A car initially traveling
V eastward turns north by
traveling in a circular
path at uniform speed
as shown in Figure P6.3.
The length of the arc
ABC is 235 m, and the
ON35.0°
car completes the turn
in 36.0 s. (a) What is the
acceleration when the car
is at B located at an angle
of 35.0? Express your
answer in terms of the
Figure P6.3
unit vectors i and j. Determine (b) the car's average speed
and (c) its average acceleration during the 36.0-s interval.
13. A roller coaster at the Six Flags
Great America amusement park
in Gurnee, Illinois, incorporates
some clever design technology
and some basic physics. Each ver-
tical loop, instead of being cir-
cular, is shaped like a teardrop
(Fig. P6.13). The cars ride on
the inside of the loop at the top,
and the speeds are fast enough
to ensure the cars remain on the
track. The biggest loop is 40.0 m
high. Suppose the speed at the
top of the loop is 13.0 m/s and
the corresponding centripetal
acceleration of the riders is 2g. (a) What is the radius of the
arc of the teardrop at the top? (b) If the total mass of a car
plus the riders is M, what force does the rail exert on the car
at the top? (c) Suppose the roller coaster had a circular loop
of radius 20.0 m. If the cars have the same speed, 13.0 m/s
at the top, what is the centripetal acceleration of the riders
at the top? (d) Comment on the normal force at the top in
the situation described in part (c) and on the advantages of
having teardrop-shaped loops.
Figure P6.13
25. A string under a
tension of 50.0 N is
used to whirl a rock
in a horizontal circle
of radius 2.50 m at
R
a speed of 20.4 m/s
on
a
frictionless
surface as shown in
Figure P6.25. As the
string is pulled in,
the speed of the rock
increases. When the
string on the table is 1.00 m long and the speed of the rock
is 51.0 m/s, the string breaks. What is the breaking strength,
in newtons, of the string?
Figure P6.25
sebeu kan/eOIoun S Jayde bgOLI
Transcribed Image Text:3. A car initially traveling V eastward turns north by traveling in a circular path at uniform speed as shown in Figure P6.3. The length of the arc ABC is 235 m, and the ON35.0° car completes the turn in 36.0 s. (a) What is the acceleration when the car is at B located at an angle of 35.0? Express your answer in terms of the Figure P6.3 unit vectors i and j. Determine (b) the car's average speed and (c) its average acceleration during the 36.0-s interval. 13. A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each ver- tical loop, instead of being cir- cular, is shaped like a teardrop (Fig. P6.13). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 m high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the cars have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops. Figure P6.13 25. A string under a tension of 50.0 N is used to whirl a rock in a horizontal circle of radius 2.50 m at R a speed of 20.4 m/s on a frictionless surface as shown in Figure P6.25. As the string is pulled in, the speed of the rock increases. When the string on the table is 1.00 m long and the speed of the rock is 51.0 m/s, the string breaks. What is the breaking strength, in newtons, of the string? Figure P6.25 sebeu kan/eOIoun S Jayde bgOLI
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