United Kingdom · Year 11 · Practice Sheet 47

1. 1.

   Find the gravitational potential energy of a 29 kg object raised 9 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Two masses 6,200 kg and 840 kg are 2 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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3. 3.

   In a triangle, a = 8, b = 14 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.

   A body starts at 13 m/s and accelerates at 2.2 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A triangle has sides a = 6 cm and b = 15 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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6. 6.

   Solve using the quadratic formula: x² + 9x + 18 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A force of 46 N acts on an area of 7.8 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   An object with initial velocity 13 m/s accelerates at 2.8 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   A cone has base radius 7 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A force of 47 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the population standard deviation of: 3, 16, 10, 16, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    Find the force needed to accelerate a 58 kg mass at 8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the gravitational potential energy of a 17 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A cylinder has radius 11 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    An object has mass 142.8 g and volume 28 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Find the momentum of a 11 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    In a triangle, a = 15, b = 14 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    A population of 1,700 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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19. 19.

    A device runs at 143 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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