Question

Question #a6587

Answer 1

Tension = 6.13 N
Period = 2.01 s

Explanation:

Draw a diagram of the situation (the mass on the angled string as seen from the side).

The procedure will be to resolve forces vertically (solve for T), then apply the centripetal force equation (solve for v) and lastly use the speed equation for uniform circular motion (solve for period).

Use trigonometry to find values for sinθ and cosθ.
`sinθ = r / l = 0.75 / 1.25 = 0.600 ⇒ θ = 36.8…º`
`cosθ = 0.800`

Resolve vertical forces
The object is not accelerating in the vertical direction so the upwards component of tension is equal to the weight.
`T cos θ = mg`
`⇒ T = (mg)/cos θ = (0.5×9.81)/0.80 = 6.13 N`

Apply the centripetal force equation
The horizontal component of the tension provides the centripetal force.
`F_c=T sin θ = (mv²)/r`
`⇒ v = sqrt((rT sin θ )/m) = sqrt((0.75 × 6.13 × 0.60 )/0.50) = 2.35 m s^(-1)`

Use the equation for speed of uniform circular motion
Remember that this "T" is the time period; it is not tension.
`v = (2 pi r) / T`
`⇒ T = (2 pi r) / v = (2 pi × 0.75) / 2.35 = 2.01 s`