High 26 Wheeled
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physics homework help?
10 points for your help.
a 0.30kg ball attached to the end of a string swings in a vertical circle having radius of 1.4 m. At the instant when the string makes an angle of 40* above the horzontal, the magnitude of the tension in the string is 3.0 N. What is the speed of the ball at this instant?
a. 2.7 m/s
b. 4.6
c.3.7
d.5.3
e.6.4
a 0.50 kg mass attached to the end of a string swings in a vertical circle radius=2m. When mass is at the highest point, the speed of the mass is 8m/s. What is the tension at this point?
a. 21 N
b. 11
c. 16
d. 26
e. 36
A wheel rotating about a fixed axis has a constant angular accof 4 rad/s^2. In a 4.0-s interval the wheel turns through 80 radians. Assunming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval?
a. 2.5 s
b. 4
c. 3.5
d. 3.0
e. 4.5
The 2nd and 3rd answers match one of the choices provided.
The first one is a bit off.
The component of the gravitational acceleration vector acting along the line of the string is 9.8*sin(x) m/sec^2 where x is the angle between the string and the horizontal. The centripetal acceleration is given by v^2/r.
1) a =2.7 m/sec is closest
At a 40 degree angle above the horizontal the gravitational acceleration component reducing the tension in the string due to the centripetal acceleration is: 9.8xsin(40) = 6.3 m/sec^2
The centripetal acceleration = v^2/r = v^2/1.4m
The net acceleration (tension) = 3N/0.3kg = 10 m/sec^2
v^2/1.4 = 10-6.3
v^2 = 5.18
v = 2.3 m/sec
2) b. 11 N
The centripetal acceleration is:
v^2/r = 8^2/2 = 32 m/sec^2
The gravitational acceleration component, at the top, which reduces the tension is 9.8 m/sec
The net acceleration is: 22.2 m/sec^2
The tension (net force) = ma = 0.5 x 22.2 = 11 N (rounded off)
3) b. 4
let v = the wheels angular speed at the start of the 4 sec
d = 80rad = v*t + 0.5 at^2
t=4sec; a = 4rad/sec^2
80 = 4v+0.5*4*(4^2) = 4v+32
20=v+4
v=16
If the wheel starts from rest:
v=a*t =16 = 4t
t = 4sec
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