A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet (0 ≤ x ≤ 5), where the variable force required is F(x) = 2000xe−x pounds. Find the work done in pushing the block the full 5 feet through the machine.

Q: A spring whose natural length is 15 cm exerts a force of 45 N when stretched to a length of 20 cm.…

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Q: Suppose a person pushes thumbtack that is 1/2 centimeter long into a bulletin board, and the force…

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Q: 1) Suppose you lift a stone that has a mass of 5.9 kilograms off the floor onto a shelf that is 1…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: An object is shot straight upward from sea level with an initial velocity of 400 ft/sec. a. Assuming…

A: Given:An object is shot straight upward from sea level with an initial velocity of 400…

Q: we consider an automobile of mass m traveling along a curved but level road. To avoid skidding, the…

A: While the automobile is in a circular motion, a centrifugal force acts on it radially outward. This…

Q: An 8.5-kg block is pushed along a horizontal rough surface by a 40-N force inclined at 20° with the…

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Q: A particle is moved along the x-axis by a force that measures 2x^3 -2 pounds at a point x feet from…

A: To determine the work done on the particle.

Q: A circular swimming pool with diameter 20 m and sides 4 m high is filled with water to a depth of 4…

A: We have to find the amount of work required to pump all of the water over the top edge of the pool.

Q: *A ball is dropped from a viscous fluid frcm rest with a resisting force numerically equal to 0.01V…

A: Given problem is :

Q: An object of mass 4.3 kg and volume 0.3 m3 is completely submerged in a tank of fluid with density…

A: As object is complementary submerged the volume of fluid displaced object V=0.3m3  fluid density…

Q: A spring exerts a force of 30 N when it is stretched 0.3 m beyond its natural length. How much work…

A: Consider the given information Force=F=30 NStretch=x=0.3 m   The relation between force and spring…

Q: The radius of a ball is claimed to be 4.5 inches, with a possible error of 0.05 inch. Use…

A: Given that,radius (r) = 4.5 inches, dr=0.05Surface area of ball is A = 4πr2= 4π(4.5)2 =4π x(20.25)A…

Q: 6. The force due to gravity on an object with mass m at a height h above the surface of the earth is…

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Q: A swimming pool is 6 feet deep at the deep end. It is 10 by 16 feet at the top and 10 by 4 feet at…

A: Consider the given information. The volume is ∆V=5ft3. The density of water is 997 kg/m³. ρ=62.4…

Q: A rope is hanging off the edge of a building that is 10 meters tall. The rope extends the entire…

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Q: A boat is being towed at the rate of 12 mi/hr. At the instant (t=0) that the towing line is cast…

A: This is differential equation problem

Q: 3. Find one approximation for the acceleration of the car, in ft/sec“, at t = 40. Show the…

A: Solution  Apply equation of motion V = U + at V = velocity at time t (ft/sec) U = velocity at time…

Q: A force of 30 newtons compresses a spring 0.3 meter from its natural length of 1.5 meters. Find the…

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Q: A large speaker that you are planning to use, has a huge diaphragm connected to a spring, the force…

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Q: The force on a particle is described by 2x 1 at a point x along the x-axis. Find the work done in…

A: topic- definite integral

Q: A cylindrical tank has a height 8 m and a radius 2 m. Suppose the water tank is half- full of water.…

A: The amount of work required to pump water from each slice out of the top of the tank,

Q: When you cough, you are using a high-speed stream of air to clear your trachea (windpipe).  During a…

A: This is what I hope the velocity isV(r) = c(3-r)r^2We don't need to know the constant since we will…

Q: A particle starts moving from the origin with the acceleration a(t)=⟨6t,4⟩, where t is measured in…

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Q: A large building shaped like a box is 50 m high with a face that is 80 m wide. A strong wind blows…

A: Given that: Pressure on the building = 150 N/ m2  Pressure function P(y) = 150 + 2y Height = 50 m…

Q: A large speaker that you are planning to use, has a huge diaphragm connected to a spring, the force…

A:

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: We need to choose correct option.

Q: A hemispherical tank of radius 8 ft. is initially filled with water. At the bottom of the tank,…

A: Let, the height is h. The volume of the hemisphere is: V=π8h2-h33 The flow satisfies the…

Q: 3. When a particle is located at a distance x feet from the origin, a force of x+ 2x pounds acts on…

A: To find the workdone we have to integrate the force x^2+2x from x=1 to x=3

Q: A body of mass 1 slug is dropped with an initial velocity of 1 ft/sec and encounters a force due to…

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Q: When you cough, you are using a high-speed stream of air to clear your trachea (windpipe). During a…

A:

Q: 7. A 16 lb weight moves in a horizontal straight line under the joint action of a constant force of…

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Q: The mass of part of a wire is x(1+ vx ) kilograms, where x is measured in meters from one end of the…

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Q: A particle is moved along the x-axis by a force that measures 5x 1 pounds at a point a feet from the…

A:

Q: 4. A car weighing 1.20 x 104 N sits on a hydraulic piston with a diameter of 0.82 m. Compressed air…

A: Use Pascal's law of Hydraulic lift to solve the question as per which Force/Area on every point of…

Q: 3. The force F newtons acting on a body at a distance x metres from a fixed point is given by: F=3x…

A: Please refer the attached image for complete solution.

Q: The rope running over two fixed cylinders carries the 4-kg mass at one end. Determine the force P…

A: Given data: 1. Rope running over fixed cylinders carries 4-kg mass at one end. 2. Force P must be…

Q: A tank is 6 m long, 4 m wide, 5 m high, and contains kerosene with density 820 kg/m3 to a depth of…

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Q: A spring exerts a force of 6 Newtons when stretched from its natural length of 4m to a length of…

A: It is given that, the spring exerts a force of 6 Newton when it is stretched from its natural length…

Q: A swimming pool is 6 feet deep at the deep end. It is 10 by 16 feet at the top and 10 by 4 feet at…

A: A swimming pool is 6 feet deep at the deep end.It is 10 by 16 feet at the top and 10 by 4 feet at…

Q: A cylindrical tube of radius 2 cm and length 3 cm contains a gas. Since the tube is spinning around…

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Q: s. When a particle is located a distance x meter from the origin, a force of F(x) = x² + 4x + 5…

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Q: You know the Excelsior must achieve 30,000 mph to reach escape velocity. The rocket’s engines are…

A: The acceleration of the rocket is, anet=10t-32 Calculate the velocity of the rocket from the above…

Q: How much work is done by a variable force F(x) = (60 − x) N that moves an object along a straight…

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Q: A horizontal cylindrical tank 4 ft in diameter and 10 ft long is full of water. Find the work one by…

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Q: A circular swimming pool has a diameter of 16 m, the sides are 4 m high, and the depth of the water…

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Q: For a given cylindrical tank, the radius is 2m and the height is 18m. The tank is filled to a depth…

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Q: 2. According to Hooke's Law, the force required to stretch a helical spring is proportional to the…

A: According to Hooke's law, F is proportional to x. where F is the force and x is the distance.…

Q: A particle is moved along the x-axis by a force that measures 4/(1 + x)² pounds at a point x feet…

A:

Q: A circular swimming pool has a diameter of 10 m, the sides are 3 m high, and the depth of the water…

A: We have to solve this problem using integral calculus.

Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.