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a) 1.256 m is correct
b) draw the rope
then the tension in the rope has a vertical component of m g (holding the mass up)
the horizontal component of tension is Fc and that makes a 15 deg angle with the rope
so
tan15 = m g / Fc
Fc = 18.3 N
c) the speed comes from
Fc = m v^2 / r
18.3 = 0.5 v^2 / 1.256
v^2 = 45.9696
v = 6.75 m/s
d)
gravity acts in the vertical direction
the mass is not moving either up or down
so
no work is done by gravity on the mass as it is swinging
b) draw the rope
then the tension in the rope has a vertical component of m g (holding the mass up)
the horizontal component of tension is Fc and that makes a 15 deg angle with the rope
so
tan15 = m g / Fc
Fc = 18.3 N
c) the speed comes from
Fc = m v^2 / r
18.3 = 0.5 v^2 / 1.256
v^2 = 45.9696
v = 6.75 m/s
d)
gravity acts in the vertical direction
the mass is not moving either up or down
so
no work is done by gravity on the mass as it is swinging
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I answered a similar question a little while ago.
You MUST learn more equations and select the one that DOES have terms that relate to what you know.
The first answer seems about right. It will be just a bit less than the 1.3 m length of string.
The cord makes and angle of 15 degrees so looking at force vectors.
Tan ( 15) = mg / (centripetal force)
You know m and c so you can easily find the centripetal force from that.
NOW you can use F = mv^2 /r
The last one is really a trick. Unless the stone is falling ( by which I mean gaining or losing height) then gravity can perform no work. Is the stone falling? ( horizontal circle )
You MUST learn more equations and select the one that DOES have terms that relate to what you know.
The first answer seems about right. It will be just a bit less than the 1.3 m length of string.
The cord makes and angle of 15 degrees so looking at force vectors.
Tan ( 15) = mg / (centripetal force)
You know m and c so you can easily find the centripetal force from that.
NOW you can use F = mv^2 /r
The last one is really a trick. Unless the stone is falling ( by which I mean gaining or losing height) then gravity can perform no work. Is the stone falling? ( horizontal circle )