Taiwan · Grade 12 · Practice Sheet 8

1. 1.

   Two masses 5,100 kg and 330 kg are 14 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 device runs at 117 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A population of 2,900 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   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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5. 5.

   A device runs at 140 V drawing 6.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the momentum of a 11 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A force of 426 N acts on an area of 1.2 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 7 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   Find the force needed to accelerate a 59 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the population standard deviation of: 6, 18, 5, 10, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    An object with initial velocity 10 m/s accelerates at 3.8 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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12. 12.

    A device runs at 135 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A 6 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    Find the force needed to accelerate a 60 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A population of 7,500 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    A 13 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Find the momentum of a 43 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A device runs at 213 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the gravitational potential energy of a 33 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A wave has frequency 51 Hz and wavelength 2.2 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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