Brazil · Ano 11 · Practice Sheet 16

1. 1.

   Two masses 8,100 kg and 110 kg are 10 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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2. 2.

   A wave has frequency 253 Hz and wavelength 2.58 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A right-angled triangle has legs of 11 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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4. 4.

   An object has mass 57.2 g and volume 26 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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5. 5.

   Find the momentum of a 43 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Solve using the quadratic formula: x² + 3x + 0 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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7. 7.

   Find the population standard deviation of: 7, 11, 17, 10, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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8. 8.

   An object has mass 73.8 g and volume 18 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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9. 9.

   A 5 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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10. 10.

    A cone has base radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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11. 11.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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12. 12.

    A body starts at 2 m/s and accelerates at 4.9 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    An object with initial velocity 9 m/s accelerates at 4 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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14. 14.

    Find the momentum of a 53 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the gravitational potential energy of a 31 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    In a triangle, a = 14, b = 16 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    A body starts at 3 m/s and accelerates at 5.3 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A force of 54 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Solve using the quadratic formula: x² − 4x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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20. 20.

    A force of 425 N acts on an area of 5.8 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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