A force of 100 newtons stretches a spring 0.5 meter beyond its natural length. How much work stretches it from natural length to 0.8 meter?

A spring has constant $k=300$ newtons per meter. How much work stretches it from 0.2 meter to 0.5 meter beyond natural length?

A force of 24 newtons stretches a spring 0.3 meter beyond natural length. How much work stretches it from 0.1 meter to 0.4 meter beyond natural length?

A force of 50 newtons compresses a spring 0.25 meter. How much work compresses it from 0.10 meter to 0.30 meter?

A spring has constant $k=120$ newtons per meter. How much work stretches it from 0.25 meter to 0.75 meter beyond natural length?

A 20-meter cable weighing 30 newtons per meter hangs from a winch. How much work lifts the whole cable to the winch?

A 12-meter chain weighing 80 newtons per meter hangs from a hook. How much work lifts only the lowest 5 meters of the chain to the hook?

A 30-meter rope weighing 10 newtons per meter hangs from a platform. How much work lifts the whole rope to a shelf 6 meters above the platform?

A 15-meter cable weighing 40 newtons per meter hangs from a crane. How much work lifts the entire cable to the crane?

A 25-meter rope weighing 12 newtons per meter hangs from a beam. How much work lifts the lowest 10 meters of rope to the beam?

A vertical cylindrical tank of radius 2 meters and height 5 meters contains water to depth 3 meters. Using $y$ from the bottom, what integral gives work to pump water over the top?

A rectangular tank 4 meters long, 2 meters wide, and 3 meters high is full of water. Using $y$ from the bottom, what integral gives work to pump it to a pipe 1 meter above the top?

A cone with vertex at the bottom, height 6 meters, and top radius 3 meters is full of water. Using $y$ from the bottom, what integral gives work to pump water over the rim?

A spherical tank of radius 2 meters is full of water and has a spout 1 meter above its top. With $y$ measured from the center, what integral gives the pumping work?

A 5-meter-long trough has triangular ends 2 meters deep and 4 meters wide at the top. It is full of water. Using $y$ from the bottom, what integral gives work to pump over the top?

A cone of height 4 meters and bottom radius 2 meters stands with its vertex at the top and is full of water. Using $y$ from the bottom, what integral gives work to pump out the top?

A vertical rectangular plate is 3 meters wide and 4 meters tall, with its top edge at the water surface. What is the fluid force on one side?

A vertical rectangular plate is 5 meters wide and 2 meters tall, with its top edge 3 meters below the water surface. What is the fluid force on one side?

A vertical triangular plate has a top edge 4 meters wide at the water surface and a vertex 3 meters below. What is the fluid force on one side?

A vertical circular plate of radius 1 meter has its center 3 meters below the water surface. What is the fluid force on one side?

A vertical trapezoidal plate has top base 2 meters at the water surface, bottom base 6 meters at depth 4 meters, and straight sides. What is the fluid force on one side?

In a pumping problem, water has weight-density $9800$ newtons per cubic meter, slice area $A(y)$, slice thickness $dy$, and lifting distance $D(y)$. What is $dW$ with units?

For a vertical submerged plate, a strip at depth $y$ has width $w(y)$ meters and height $dy$. Water has weight-density $9800$ newtons per cubic meter. What is $dF$?

For a spring obeying $F=kx$ with $k$ in newtons per meter, what differential work is done during an additional stretch $dx$ at extension $x$?