Centripetal and Centrifugal Force and Acceleration
Assignment. (3)
(1a)
Centripetal force is the name given to a force which produces centripetal acceleration. Any motion in a curved path represents accelerated motion, and requires a force directed towards the centre of curvature of the path. Centripetal force means “centre seeking” force.
Centripetal Force is the radial force which acts ON a rotating mass and Centrifugal Force is the radial force which is exerted BY a rotating mass.
(1b)
Centripetal Acceleration is the inwards acceleration necessary to maintain circular motion. If a point moves at uniform speed in a circular path, its direction is continually changing and, therefore, though its speed is constant its velocity is changing. Acceleration is defined as “rate of change of velocity with respect to time”
Centripetal Acceleration (a) = v² (Linear Velocity)
r
Centripetal Acceleration (a) = w²r (Angular Velocity)
(2)a
Mass 1000kg (m)
Radius of Curve 45m (r)
Coefficient Friction 0.7 (u)
Track of Vehicle 1.5m (d)
Centre of Gravity 0.68m (h)
Acceleration (force of gravity) 9.81 m/s² (g)
Without skidding outwards,
Centrifugal force = Frictional resistance to skidding = m v² = u m g
r
Max Speed v = √u g r
=√ 0.7 x 9.81 x 45
=√ 309.015
= 17.5788 m/s
Convert to km/h = (17.5788m/s x 3.6) = 63.3 km/h
Without overturning,
Overturning moment = Righting moment = m v²h = m g d
r 2
Max Speed V = √g r d
2 h
=√ 9.81 x 45 x 1.5
2 x 0.68
=√ 225.1395
= 15.0046 m/s
Convert to km/h = (15.0046m/s x 3.6) = 54 km/h
(2)b
Rotating Bobs 250g (each)
Spring Strength 8 kN/m
Centre Mass of Bob 160mm radius (resting)
Balance of forces = F + R = Mw²r
At Engagement,
F = Stiffness x Extension
= 8 x 1000 x 12
1000
= 96 N
(Radius of Rotation r= 160 + 12 = 177mm (convert to metres 177 = 0.177m)...