Ireland · Year 12 · Practice Sheet 4

1. 1.

   Find the gravitational potential energy of a 5 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A force of 155 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A force of 64 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A cone has base radius 2 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Find the gravitational potential energy of a 10 kg object raised 23 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A device runs at 231 V drawing 6.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A force of 70 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A current of 5 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Solve using the quadratic formula: x² + 1x + 0 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A wave has frequency 371 Hz and wavelength 4.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A force of 24 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    €800 is invested at 5% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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14. 14.

    Find the population standard deviation of: 14, 19, 5, 8, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Find the force needed to accelerate a 6 kg mass at 0.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the momentum of a 40 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    €1,600 is invested at 3% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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18. 18.

    A force of 31 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A cone has base radius 7 cm and height 24 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 body starts at 14 m/s and accelerates at 5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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