Verified answer

Answer:

Explanation:

Here's a step-by-step explanation:

1. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its speed.

2. The percentage error in a calculated quantity is the sum of the percentage errors in the quantities used to calculate it.

3. Let's say the percentage error in mass (m) is represented as Δm/m * 100% = 20%, and the percentage error in speed (v) is represented as Δv/v * 100% = 10%.

4. Since kinetic energy depends on the square of the speed, the percentage error in v^2 is 2 * Δv/v * 100% = 20%.

5. So, the percentage error in kinetic energy (KE) is given by:

ΔKE/KE * 100% = (Δm/m + 2 * Δv/v) * 100%

= (20% + 20%) = 40%

This means that if there is a 10% error in the measurement of speed and a 20% error in the measurement of mass, then there will be a 40% error in the determination of kinetic energy. Therefore, the correct answer is 40%, not 45.2%. I hope this helps!

It's difficult for me to say exactly how you arrived at the answer of 45.2% without seeing your calculations. However, one common mistake that students make when calculating percentage errors is to add the percentage errors directly instead of using the formula for the percentage error in a calculated quantity. Another possibility is that you may have made an arithmetic error while performing the calculations. If you could share your calculations with me, I would be happy to take a look and help you identify where you might have gone wrong.

Answer:

The percentage error in the determination of kinetic energy is 40%.

Explanation:

To find the percentage error in the determination of kinetic energy, we need to understand how kinetic energy (KE) is calculated and how errors in measurements affect it.

The formula for kinetic energy is given by:

[tex]KE = ( \frac{1}{2} ) \times m \times v^2[/tex]

where m is the mass of the object and v is its speed.

Let's consider the percentage errors in the measurement of mass (Δm) and speed (Δv) as follows:

- Percentage error in mass = 20%

- Percentage error in speed = 10%

Now, let's calculate the absolute errors in mass (Δm) and speed (Δv) using the given percentage errors:

Absolute error in mass (Δm)

[tex]= ( \frac{20}{100} ) \times m[/tex]

Absolute error in speed (Δv)

[tex]= ( \frac{10}{100} ) \times v[/tex]

Now, to find the percentage error in kinetic energy (ΔKE), we use the formula:

[tex]\Delta KE = [( \frac{\Delta m }{ m}) + (2 \times \frac{ \Delta v}{v})] \times 100[/tex]

Substitute the values of Δm and Δv:

[tex]\Delta KE = [( \frac{20}{100} ) \times \frac{m}{m} + 2 \times ( \frac{10}{100} ) \times \frac{v}{v} ] \times 100[/tex]

Simplify:

ΔKE = [0.2 + 0.2] × 100

ΔKE = 0.4 × 100

ΔKE = 40%

So, the percentage error in the determination of kinetic energy is 40%.

However, it seems that there might have been an error in the given answer, which is 45.2%. The correct percentage error, as calculated above, is 40%.

Similar Questions:

https://brainly.in/question/56807969

https://brainly.in/question/9550706

#SPJ1