Portugal · Ano 12 · Practice Sheet 22

1. 1.

   A device runs at 169 V drawing 1.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the gravitational potential energy of a 37 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   In a triangle, a = 16, b = 6 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   Find the momentum of a 45 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Solve using the quadratic formula: x² − 2x + 0 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   A force of 330 N acts on an area of 2.6 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the momentum of a 16 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A body starts at 11 m/s and accelerates at 2 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   In a triangle, a = 15, b = 16 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A body starts at 4 m/s and accelerates at 5.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A force of 91 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A 38 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Two masses 7,200 kg and 830 kg are 13 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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14. 14.

    Find the momentum of a 37 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 9 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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16. 16.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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17. 17.

    A device runs at 72 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the force needed to accelerate a 33 kg mass at 2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A cone has base radius 12 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A triangle has sides a = 13 cm and b = 16 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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