A worker pushes a 50 kg crate a distance of 8 meters across a level floor with a constant horizontal force of 120 N. How much work does the worker do on the crate?

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An ideal spring with a spring constant $k = 400 \text{ N/m}$ is compressed by $0.15 \text{ m}$ from its equilibrium position. How much work is done by the spring as it expands back to equilibrium ($x=0$)?

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A particle is subjected to a force $F(x) = (3x^2 - 2x + 5) \text{ N}$. Calculate the work done by this force as the particle moves from $x = 1 \text{ m}$ to $x = 3 \text{ m}$.

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A 2 kg ball is dropped from rest from a height of 10 meters. Ignore air resistance. What is its velocity just before it hits the ground? ($g = 9.8 \text{ m/s}^2$)

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A roller coaster car (mass $m$) starts from rest at the top of a hill of height $h$. It then enters a circular loop of radius $R$. Assuming no friction, what is the minimum height $h$ required so that the car doesn't fall off the track at the very top of the loop?

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A 5 kg block slides down a $30^\circ$ incline that is 4 meters long. It starts from rest at the top. The coefficient of kinetic friction is $\mu_k = 0.25$. Use energy methods to find its speed at the bottom of the incline.

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An electric motor lifts a 1500 kg elevator cab 20 meters upward at a constant speed in 12 seconds. What is the average power output of the motor in Watts and Horsepower? ($1 \text{ hp} \approx 746 \text{ W}$)

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A car engine applies a constant forward thrust force of 3000 N to maintain a steady highway speed of $25 \text{ m/s}$ (approx 90 km/h) against air resistance and friction. What is the instantaneous power output of the engine?

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A water pump is rated at $5.0 \text{ kW}$ of electrical power input. It is used to pump water from a well 15 meters deep up to a storage tank at ground level. If it pumps 1200 kg of water in 1 minute, what is the mechanical efficiency of the pump system?

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