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# Centripetal Force and Spring Force

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```Centripetal Force and Spring Force
Centripetal Force
пЃµ
Recall that centripetal acceleration is
directed toward the center of a circle.
вЂ“ вЂњCentripetalвЂќ = вЂњcenter-seekingвЂќ.
вЂ“ ac = v2/r = пЃ·2r
пЃµ
Centripetal force, Fc
вЂ“ Force that keeps an object on a circular path.
F = ma
mv2
пЃµ Fc = mac =
= mпЃ·2r
r
пЃµ
Centripetal Force
Fc
Centripetal Force
Centripetal Force
пЃµA
1500-kg vehicle makes a turn
whose radius is 20.0 meters while
traveling at 10.0 m/s. What
centripetal force acted on the
vehicle?
вЂ“ Fc
вЂ“ Fc
вЂ“ Fc
вЂ“ Fc
=
=
=
=
mac
mv2/r
(1500 kg)(10.0 m/s)2 / 20.0 m
7500 N
Centripetal Force
Mass = 10 kg; Radius = 1 m
Centripetal Force (N)
700
600
500
400
300
200
100
0
0
20
40
60
Angular Velocity (rpm)
80
Centripetal Force
Radius = 1 m; Angular Velocity = 30 rpm
Centripetal Force (N)
1000
800
600
400
200
0
0
20
40
60
Mass (kg)
80
100
Centripetal Force
Mass = 10 kg; Angular Velocity = 30 rpm
Centripetal Force (N)
1000
800
600
400
200
0
0
2
4
6
8
10
Spring Force
пЃµ
пЃµ
Fs = force exerted by a spring when it is stretched.
Fs = kx.
вЂ“ k = spring constant (N/m)
пЃµ Unique for every spring.
вЂ“ x = stretch (m)
пЃµ How far spring is stretched past its equilibrium length.
пЃµ For example, if spring is 10 cm long when relaxed and
15 cm long when stretched, then x = 5 cm.
пЃµ Relationship holds true for relatively small stretches.
пЃµ For big stretches spring can become deformed.
Spring Force
Force (N)
Spring Constant = 50 N/m
400
350
300
250
200
150
100
50
0
0
2
4
Stretch (m)
6
8
Spring Force
пЃµA
certain spring has a constant k =
5.0 N/m and is 50.0 cm long when
relaxed. How much force is required
to stretch the spring to 100. cm
long?
вЂ“ Change cm to m.
пЃµ 50.
cm = 0.50 m
вЂ“ Fs = kx
вЂ“ Fs = (5.0 N/m)(0.50 m) = 2.5 N
```
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