1. A 0.1-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 50 cm and ball’s angular speed is 4 rad s-1. What is the magnitude of the centripetal force?
Known :
Mass (m) = 100 gram = 100/1000 kg = 1/10 kg = 0.1 kg
Angular speed (ω) = 4 radians/second
Radius (r) = 50 cm = 50/100 m = 0.5 m
Wanted : Centripetal force
Solution :
Centripetal force is net force which produces centripetal acceleration :
∑F = m ar
∑F = m v2/r = m ω2 r
∑F = net force = centripetal force, m = mass, v = speed, ω = angular speed, r = radius
∑F = m ω2 r = (0.1)(4)2 (0.5) = (0.1)(16)(0,5) = 0.8 Newton
2. A ball is revolving uniformly in a horizontal circle. If the speed changed to four times the initial value, what is the magnitude of centripetal force…..
Known :
Mass = m
Speed = v
Initial speed = vo
Radius (r) = r
Wanted: Magnitude of centripetal force
Solution :
3. A banked curve of radius R is designed so that a car traveling at speed 12 ms–1 can negotiate the turn safely. The coefficient of static friction between car and road = 0.4. What is radius R. Acceleration due to gravity (g) = 10 ms–2.
Known :
Speed (v) = 12 m/s
Coefficient of static friction (μs) = 0.4
Acceleration due to gravity (g) = 10 m/s2
Wanted: Radius (R)
Solution :
[wpdm_package id=’501′]
- Mass and weight
- Normal force
- Newton’s second law of motion
- Friction force
- Motion on a horizontal surface without friction force
- The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force
- Motion on the inclined plane without friction force
- Motion on the rough inclined plane with the friction force
- Motion in an elevator
- The motion of bodies connected by cord and pulley
- Two bodies with the same magnitude of accelerations
- Rounding a flat curve – dynamics of circular motion
- Rounding a banked curve – dynamics of circular motion
- Uniform motion in a horizontal circle
- Centripetal force in uniform circular motion
