Kinetic energy questions and answers

Worked solution

1. $E_k = 0.5 \times 2 \times 3^2 = 0.5 \times 2 \times 9 = 9$ J

Worked solution

1. $E_k = 0.5 \times 1200 \times 20^2 = 0.5 \times 1200 \times 400 = 240\,000$ J

Worked solution

1. $E_k = 0.5 \times 0.06 \times 50^2 = 0.5 \times 0.06 \times 2500 = 75$ J

Worked solution

1. $m = \dfrac{2 \times 1350}{6^2} = \dfrac{2700}{36} = 75$ kg

Worked solution

1. $v^2 = \dfrac{2 \times 16}{0.5} = 64$
2. $v = \sqrt{64} = 8$ m/s

Worked solution

1. $36 \div 3.6 = 10$ m/s
2. $E_k = 0.5 \times 900 \times 10^2 = 45\,000$ J

Worked solution

1. $E_k \propto v^2$, so doubling $v$ multiplies $E_k$ by $2^2 = 4$.
2. Check: $\tfrac{1}{2}m(20^2) \div \tfrac{1}{2}m(10^2) = 400 \div 100 = 4$

Worked solution

1. At 25 m/s: $0.5 \times 1000 \times 625 = 312\,500$ J
2. At 15 m/s: $0.5 \times 1000 \times 225 = 112\,500$ J
3. Lost: $312\,500 - 112\,500 = 200\,000$ J