Colombia · Grado 11 · Practice Sheet 27

1. 1.

   Two masses 4,700 kg and 660 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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2. 2.

   In a triangle, a = 8, b = 12 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   Find the force needed to accelerate a 48 kg mass at 4.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   An object has mass 211.7 g and volume 29 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A current of 1 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A right-angled triangle has legs of 8 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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7. 7.

   A body starts at 12 m/s and accelerates at 1.1 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   An object with initial velocity 5 m/s accelerates at 2.1 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the force needed to accelerate a 12 kg mass at 1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the momentum of a 29 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    An object has mass 39.6 g and volume 12 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A body starts at 7 m/s and accelerates at 1.5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the gravitational potential energy of a 8 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A cylinder has radius 6 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Find the force needed to accelerate a 47 kg mass at 1.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the momentum of a 31 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A population of 4,800 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A body starts at 20 m/s and accelerates at 4.8 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    $2,600 is invested at 4% 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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20. 20.

    A force of 29 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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