NEET Work Energy and Power — Set 17

Question 1

A $ 0.5 \, \text{g} $ drop falls from $ 350 \, \text{m} $ and hits the ground at $ 17 \, \text{m/s} $. What is the work done by air resistance? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Work by gravity $ W_g = mgh = 0.0005 \times 10 \times 350 = 1.75 \, \text{J} $. Final $ K = \frac{1}{2} \times 0.0005 \times 17^2 = 0.07225 \, \text{J} $. $ K_f = W_g + W_r \Rightarrow 0.07225 = 1.75 + W_r \Rightarrow W_r = -1.67775 \, \text{J} \approx -1.68 \, \text{J} $.

Question 2

A $ 1300 \, \text{kg} $ car at $ 18 \, \text{m/s} $ hits a spring ($ k = 8 \times 10^3 \, \text{N/m} $). What is the maximum compression?

Accepted Answer

Initial $ K = \frac{1}{2} \times 1300 \times 18^2 = 210600 \, \text{J} $. Spring energy $ \frac{1}{2} k x_m^2 = 210600 \Rightarrow 4000 x_m^2 = 210600 \Rightarrow x_m = \sqrt{52.65} \approx 7.26 \, \text{m} $.

Question 3

A $ 2 \, \text{kg} $ block with initial speed $ 5 \, \text{m/s} $ encounters a force $ F = \frac{-1}{x} \, \text{N} $ from $ x = 0.5 \, \text{m} $ to $ x = 2.5 \, \text{m} $. What is the final speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 2 \times 5^2 = 25 \, \text{J} $. Work $ W = \int_{0.5}^{2.5} \frac{-1}{x} \, dx = -\ln(x) \Big|_{0.5}^{2.5} = -\ln(2.5/0.5) = -\ln 5 \approx -1.61 \, \text{J} $. Final $ K = 25 - 1.61 = 23.39 \, \text{J} \Rightarrow v_f = \sqrt{\frac{2 \times 23.39}{2}} \approx 4.83 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 17

Q1. A \( 0.5 \, \text{g} \) drop falls from \( 350 \, \text{m} \) and hits the ground at \( 17 \, \text{m/s} \). What is the work done by air resistance? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 1300 \, \text{kg} \) car at \( 18 \, \text{m/s} \) hits a spring (\( k = 8 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Q3. A \( 2 \, \text{kg} \) block with initial speed \( 5 \, \text{m/s} \) encounters a force \( F = \frac{-1}{x} \, \text{N} \) from \( x = 0.5 \, \text{m} \) to \( x = 2.5 \, \text{m} \). What is the final speed?

Q4. A force \( F = 12x \, \text{N} \) acts from \( x = 0 \) to \( x = 3 \, \text{m} \). What is the work done?

Q5. A force starts at \( 85 \, \text{N} \) over \( 5 \, \text{m} \), then decreases linearly to \( 25 \, \text{N} \) over \( 5 \, \text{m} \). What is the total work done?

Q6. A spring (\( k = 400 \, \text{N/m} \)) is stretched by \( 0.05 \, \text{m} \). What is the stored potential energy?

Q7. A motor lifts a \( 1900 \, \text{kg} \) load at \( 3 \, \text{m/s} \) against \( 5000 \, \text{N} \) friction. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A force \( F = 4x^2 \, \text{N} \) acts from \( x = 0 \) to \( x = 2 \, \text{m} \). What is the work done?

Q9. A spring (\( k = 350 \, \text{N/m} \)) is stretched by \( 0.25 \, \text{m} \). What is the stored potential energy?

Q10. A force starts at \( 70 \, \text{N} \) over \( 4 \, \text{m} \), then decreases linearly to \( 30 \, \text{N} \) over \( 8 \, \text{m} \). What is the total work done?