Argentina · Grado 12 · Practice Sheet 4

1. 1.

   Two masses 5,300 kg and 660 kg are 20 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.

   Find the gravitational potential energy of a 50 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A cone has base radius 8 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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4. 4.

   Find the momentum of a 59 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A 36 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A body starts at 1 m/s and accelerates at 5.7 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A force of 11 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 12 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A device runs at 29 V drawing 9.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A 22 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A body starts at 1 m/s and accelerates at 3.7 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A device runs at 15 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 339 N acts on an area of 2.6 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    An object with initial velocity 3 m/s accelerates at 1.7 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A force of 35 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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17. 17.

    A population of 5,400 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A force of 43 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A wave has frequency 245 Hz and wavelength 0.88 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    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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