Intro to Calculating Work Practice Problems

A skater is being pulled a distance of 30.0 m by two bikers on a flat road. The first biker applies a 100.0 N force due west and the second biker a force of 100.0 N due north. The net work done on the skater is :

James is pulling horizontally a 65 kg fridge along a 10 m straight horizontal path. The motion of the fridge is assumed uniform. How much work is done on the fridge If the coefficient of kinetic friction is 0.4?

A toy box has a weight of 145 N. A child applies a force to the box parallel to the level floor moving it 2 m at a speed of 0.2 m/s. If the coefficient of kinetic friction between the box and the floor is 0.25, calculate the work done by (i) gravitational force and (ii) normal force on the box.

A constant horizontal force F is applied to a 60.0 kg desk, moving it 6 m on a horizontal floor with zero acceleration. The coefficient of kinetic friction between the desk and the floor is 0.5. The work done on the desk by the force F is:

In a certain theatre, a 250.0 kg piano is pushed 3.0 m  on a rough horizontal surface. The coefficient of kinetic friction between the piano and the surface is 0.4. The magnitude of the force needed to move the piano at a constant speed is:

A student wishes to move a 15.0 kg wooden desk at a constant speed on a 10 m horizontal concrete surface by applying a force parallel to the surface. If the coefficient of kinetic friction between the wood and concrete is 0.3, the work done by friction on the desk will be:

A crane lifts an 850kg container at a constant upward acceleration of 1.20 m/s² for 3.5 m. Assume the container was initially at rest. Calculate the work done by the crane in lifting the container. 

An electric water pump is used to lift water to a tank.  Assume pumping of salty water with a density ρ = 1010 kg/m³ and consider the pump raising a volume element, V = 250L to the tank. Take water to be a non-viscous liquid that does not experience friction from the walls of a pipe. The pump exerts an upward force on the water, lifting the water to a tank for a total height of h = 80 m. Use the given variables to determine the work done by the pump.

A box is pulled across a bench. Four forces are applied to the box. The box moves a distance 0.8 m as shown. Determine the work done by each force.

It is common for friction to create a net torque that decelerates rotating objects. When objects rotate in fluids, objects experience drag force that has the same consequences as friction. Drag has a characteristic nature where it is nearly negligible at low rotational speeds and increases very fast at high rotational speeds. Using a circular rod of diameter, D, and with a length, Y, rotating at an angular velocity, ω, in a fluid whose density is ρ. Taking the drag coefficient to be C and assuming it is constant at all points on the rod for the rotation on an axle through one of its ends and perpendicular to the length, derive an expression of the rod's drag torque magnitude. Hint: Consider the drag force on an element dr located at a distance r from the rotational axis.

A search and rescue helicopter lifts a distressed sailor of mass 85 kg using a cable from point A with cartesian coordinates ( x_A = 3.5 × 10³ m; y_A = 0 m) to point B with cartesian coordinates ( x_B = 2.2 × 10³ m; y_B = 18.5 m). Calculate the work done by the gravitational force during this rescue mission. Assume that the sailor is lifted up at constant speed.

A 70.0-kg hiker climbs a 30.0 m tall mountain steadily. Determine the hiker's work.

Assess the work involved in sweeping a 12 m × 22 m courtyard using a 52 cm wide broom. Assume a force of 18 N is applied horizontally.

A block is moving along the x-axis. F(x) = Bx^1/2 gives the force acting on the block. Given that B = 12.0 N/m^1/2, How much work does the force do in moving the block from x = 0.0 to x = 5.0 m?

In a construction project, the first layer of bricks is to be placed 30.0 cm above the ground, and each of the remaining three layers is stacked 25.0 cm above the previous one. If the average brick has a mass of 2.5 kg with a height of 7.5 cm, and each layer requires 100 bricks to complete, how much work is required to stack all the bricks, assuming the bricks are initially all on the ground?

In the illustration below, a worker utilizes a hand cart to lift heavy crates. If the friction and the mass of the cart are neglected, and it is assumed that the work output equals the work input, determine the ratio of the output force (F_o) to the input force (F_i ) concerning the distances L_i and L_o from the center of the cart's wheels.

A man is trying to drive a staple into a bundle of paper with a 1.5 kg block of iron. He puts the bundle on the floor, places the staple on top of it, and then lets the block fall onto the staple from a height of 0.55 m. Calculate the maximum work the block can do on the staple in this manner. Explain why, it would be more effective to add his own force to the block as it falls rather than just "letting it fall".  

A satellite of mass 1200 kg was initially at rest in space at 14000 km above the Mars' surface. Suddenly, it fell vertically down to Mars. Calculate the work done by the force of gravity in moving the satellite to Mars' surface from its initial position. (Assume the mass and radius of Mars are 6.4 x 10²³ kg and 3.4 x 10⁶ m, respectively.)

A luggage cart with mass $m$ is placed on an airport's moving walkway moving at speed $v$. The kinetic friction coefficient between the cart and walkway is $\mu_{k}$ . Over time $t$, the cart stops moving relative to the walkway, traveling distance $d=\frac12\frac{v^2}{\mu_{k}g}$ . How much of the work done by the walkway's motor is used against friction and how much to accelerate the luggage?

A car is being pulled by a tow truck along a straight road. The tow truck exerts a constant force $\overrightarrow{F}$ = (250 î + 150 ĵ) N on the car as it moves along the road. If the car experiences a displacement $\overrightarrow{d}$ = (120 î + 80 ĵ) m, determine the work done by the tow truck using: (i) W = Fd cosθ ; (ii) W = F_xd_x + F_yd_y .

A worker navigates a handcart across the warehouse floor. Initially, the cart smoothly glides over the polished surface as the worker applies a horizontal force of 40 N, moving it to a distance of 8.0 m. Subsequently, encountering a rough patch, one of the cart's wheels malfunctions, requiring the worker to exert a force of 60 N at a 25° angle from the horizontal for the next 5.0 m. Finally, returning to the smooth floor, the worker pushes the cart for the remaining 7.0 m with a horizontal force of 40 N. Calculate the total work done by the worker on the handcart throughout the journey.

A 0.016 kg rubber bullet was fired horizontally at a shooting target 18 m away. After the bullet left the barrel, it had an initial speed of 216 km/h. Upon reaching the target, its speed dropped by 15%. Ignoring gravity, calculate the average drag force due to air on the bullet.

A 47 kg dog accidentally jumped off a helicopter at a height of 410 m. Fortunately, it landed in a haystack, burying itself 1.5 m inside, and survived. Given that its terminal velocity was 49 m/s, calculate the work done on the dog by air resistance during its fall. For simplicity, assume that the dog was a particle.

Suppose an object is subjected to a force F(y) as it moves along the y-axis from y=0 to y=2.0m. The force F(y) is described by the function: F(y) =$\frac{3}{\sqrt{5y}}$ Nm^1/2. Determine the work done by this force.

A sturdy steel cable is positioned horizontally on the platform as depicted in the illustration. Initially, 3.0 m of the cable rests on the platform, while 2.0 m dangles vertically over the platform's edge. At this juncture, the force on the dangling section is adequate to initiate the motion of the entire cable over the edge. Once the cable commences its descent, any kinetic friction is insignificant. Determine the work done by gravity on the cable as it descends from the point where 3.0 m remains on the platform until the entire cable is hanging vertically.(Assume a linear weight density of 30 N/m for the cable.)

A drone weighing 0.21 kg experiences two forces while in flight: F̄₁ = (2.50î - 1.80ĵ + 1.70k̂) N and F̄₂ = (-1.70î + 2.20 ĵ) N. When the two forces act on it, the drone's displacement vector is d̄ = (7.0î + 9.0ĵ + 4.0k̂) m. Determine the total work done on the drone by these forces.