A weight with mass 100 g is connected to a rotatable rob through two inelastic strings. Both strings are 50 cm. If you extend both strings..?
they create the angle 45 degrees against the rod. When the rob rotates the weight moves in a circular path.
What is the tension force in the lower string when the weight is rotating with 1 lap/second?
- Steve4PhysicsLv 76 months ago
Call the upper string 1 and the lower string 2.
50cm = 0.5m, so radius of motion is: r = 0.5cos(45º) = 0.3536m
ω = 1lap/s = 2π rad/s = 6.283 rad/s
Centripetal force = mω²r = 0.1 * 6.283² * 0.3536 = 1.396N
Centripetal force is the sum of the horizontal components of T₁ and T₂:
T₁cos(45º) + T₂cos(45º) = 1.396
Divide through by cos(45º):
T₁ + T₂ = 1.974 (equation 1)
Vertically the forces balance:
Upwards force = total downwards force
T₁sin(45º) = T₂sin(45º) + mg
T₁ - T₂ = mg/sin(45º)
. . . . . . = 0.1*9.8/sin(45º)
. . . . . . .= 1.386 (equation 2)
Subtract equation 2 from equation 1:
2T₂ = 1.974 - 1.386
T₂ = 0.294N
You should probably round to 1 sig. fig. (giving 0.3N) or possibly 2 sig. figs (giving 0.29N).
I used g = 9.8m/s². If you need a different value it will alter the final answer slightly.
- 6 months ago
1 lap/second => f=1
F - centripetal force
T - tension of bottom string
T' - tension of top string
ω(angular frequency)=2πf since f is 1 ω=2π
From geometry we can conclude
Tcos45°+T'cos45°=F and since value of sin45° is the same as of the cos45° we can replace it, thus getting two equations with two unknonws
expressing T' from the first equation T'=T+mg/(sin45°)
and substituting it into the second Tsin45°+Tsin45°+mgsin45°/(sin45°) = 4Rmπ^2
2Tsin45°+mg = 4Rmπ^2
2Tsin45° = 4Rmπ^2-mg
sin45° is equal to √2/2 thus giving
√2T = 4Rmπ^2-mg
substituting the values we get
- JOHNLv 76 months ago
T = tension in lower string, T’ = tension in upper string.
Since motion is wholly in a horizontal plane,
T’ – T = 0.1g....(1)
For motion in a horizontal circle
T’cos45° + T cos45° = 0.1 x (2π)² = 0.4π²....(2)
Substituting for T’ from (1) in (2)
T + 0.1g + T = (0.4π²)/ cos45°
T = [(0.4π²)/ cos45° - 0.1g]/2
T = 2.3N.