Question

kinetic energy and potential energy

1. calculate the kinetic energy of a 45 gram golf ball travelling at: (a) 20. m/s, (b) 40. m/s, (c) 60. m/s
2. how fast must a 1000. kg car be moving to have a kinetic energy of:

(a) $2.0 \times 10^{3}$ j,
(b) $2.0 \times 10^{5}$ j,

1. how high would you have to lift a 1000. kg car to give it a potential energy of:

(a) $2.0 \times 10^{3}$ j,
(b) $2.00 \times 10^{5}$ j,

1. calculate the potential energy of a 5.00 kg object sitting on a 3.00 meter high ledge.
2. a 10.0 kg rock is at the top of a 20.0 m. tall hill. how much potential energy does it have?
3. a 25 n object is 3.0 meters up. how much potential energy does it have?
4. how high up is a 3.00 kg object that has 300. j of energy?
5. a 4.00 kg rock is rolling 10.0 m/s. find its kinetic energy.
6. an 8.0 kg cat is running 4.0 m/s. how much kinetic energy does it have?

Explanation:

Problem 1

Step1: Convert mass to kg

$m = 45\ \text{g} = 0.045\ \text{kg}$

Step2: Kinetic energy formula

$KE = \frac{1}{2}mv^2$

Step3: Calculate for 20 m/s

$KE = \frac{1}{2} \times 0.045 \times 20^2 = 9\ \text{J}$

Step4: Calculate for 40 m/s

$KE = \frac{1}{2} \times 0.045 \times 40^2 = 36\ \text{J}$

Step5: Calculate for 60 m/s

$KE = \frac{1}{2} \times 0.045 \times 60^2 = 81\ \text{J}$

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Problem 2

Step1: Rearrange KE for velocity

$v = \sqrt{\frac{2KE}{m}}$

Step2: Calculate for $2.0 \times 10^3\ \text{J}$

$v = \sqrt{\frac{2 \times 2.0 \times 10^3}{1000}} = 2.0\ \text{m/s}$

Step3: Calculate for $2.0 \times 10^5\ \text{J}$

$v = \sqrt{\frac{2 \times 2.0 \times 10^5}{1000}} = 20\ \text{m/s}$

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Problem 3

Step1: Rearrange PE for height

$h = \frac{PE}{mg}$, use $g=9.8\ \text{m/s}^2$

Step2: Calculate for $2.0 \times 10^3\ \text{J}$

$h = \frac{2.0 \times 10^3}{1000 \times 9.8} \approx 0.20\ \text{m}$

Step3: Calculate for $2.00 \times 10^5\ \text{J}$

$h = \frac{2.00 \times 10^5}{1000 \times 9.8} \approx 20.4\ \text{m}$

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Problem 4

Step1: Gravitational PE formula

$PE = mgh$

Step2: Substitute values

$PE = 5.00 \times 9.8 \times 3.00 = 147\ \text{J}$

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Problem 5

Step1: Apply PE formula

$PE = mgh$

Step2: Substitute values

$PE = 10.0 \times 9.8 \times 20.0 = 1960\ \text{J}$

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Problem 6

Step1: PE formula for weight (W=mg)

$PE = Wh$

Step2: Substitute values

$PE = 25 \times 3.0 = 75\ \text{J}$

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Problem 7

Step1: Rearrange PE for height

$h = \frac{PE}{mg}$

Step2: Substitute values

$h = \frac{300}{3.00 \times 9.8} \approx 10.2\ \text{m}$

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Problem 8

Step1: Apply KE formula

$KE = \frac{1}{2}mv^2$

Step2: Substitute values

$KE = \frac{1}{2} \times 4.00 \times 10.0^2 = 200\ \text{J}$

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Problem 9

Step1: Apply KE formula

$KE = \frac{1}{2}mv^2$

Step2: Substitute values

$KE = \frac{1}{2} \times 8.0 \times 4.0^2 = 64\ \text{J}$

Answer:

1. (a) $9\ \text{J}$, (b) $36\ \text{J}$, (c) $81\ \text{J}$
2. (a) $2.0\ \text{m/s}$, (b) $20\ \text{m/s}$
3. (a) $0.20\ \text{m}$, (b) $20.4\ \text{m}$
4. $147\ \text{J}$
5. $1960\ \text{J}$
6. $75\ \text{J}$
7. $10.2\ \text{m}$
8. $200\ \text{J}$
9. $64\ \text{J}$