Net Work & Work-Energy Theorem Practice Problems

An airplane pallet of mass 35.0 kg is pushed with a constant force of magnitude 320 N up a 3.0 m wooden ramp. The applied force forms a 10° angle above the ramp and the ramp makes an angle of 25° with the horizontal. The coefficient of kinetic friction between the pallet and the ramp is 0.35. Calculate the magnitude of the change in internal energy of the pallet-ramp system due to friction. 

A 2.5-kg object subject to the position-dependent force shown in the figure below moves in a straight line on a horizontal frictionless plane. At the position x = 0 m, the velocity of the object is -4.0 m/s. Determine the position where the object reverses its direction.

A blue block and a yellow block are pushed by a constant force through the same distance. The blue block, which has a mass of 100 g, is launched at a speed of 20 m/s. If the yellow block is launched at a speed of 40 m/s, what is the mass of the yellow block?

How much work is required to accelerate a 250 g block from rest to 15 m/s if a force of 22 N is applied in the direction of motion?

A 2.00-N ball is thrown from the ground upwards to the air. At 10.0 m above the ground, you measure its speed as 20.0 m/s. Calculate the ball's highest point using the work-energy theorem.

A 2.00-N ball is thrown from the ground upwards to the air. At 10.0 m above the ground, you measure its speed as 20.0 m/s. Calculate the ball's initial speed using the work-energy theorem.

A box with a mass of 2.0 kg moves along an irregular horizontal surface. It is traveling at 3.0 m/s at point X but has slowed to 2.25 m/s at point Y. Calculate the work needed to put into the box as it is traveling between points X and Y.

As shown in the figure, a skateboarder with a mass of 70 kg is skating at a speed of 7.0 m/s when he approaches the curved road. He allows the skateboard to move freely without any special effort. If we neglect the rolling friction, determine the skateboarder's speed when he reaches the top of the road on the other side.

A construction worker drops a 2 kg hammer from the top of a building, which is 40 m tall. The hammer strikes a pile driver that is resting on the ground, and the pile driver drives a steel beam into the ground. If the beam is driven 25 cm into the ground by the impact, what is the magnitude of the average force that the hammer exerts on the pile driver?

A boy is riding his bicycle moving north at 6.0 m/s. There is wind flowing in the direction 30 degrees west of south exerting a force of 4.5 N. Consider there is no rolling friction but static friction which will save the boy from skidding sideways. Calculate the minimum value of the static friction coefficient that will help move towards the north. Consider the combined mass of the boy and his bicycle is 35 kg.

A rollercoaster car with a mass of 500 kg is released from the top of a hill with a height of 50 m. As the car descends down the hill, it increases its speed from 0 m/s to 30 m/s. If the total distance travelled by the rollercoaster is 100 m, what is the total work done by gravity on the rollercoaster car?

During a punching challenge, a boxer punches a horizontal spring which is mounted on a vertical pole. The spring compresses by 10.0 cm. Calculate the force of the punch by the boxer if the spring constant is 600 N/m.

A rope tensioned at 165 N is used to lift an initially stationary 9.0 kg bucket vertically upward from a well. Determine the speed of the bucket when it has covered a height of 6.5 m using work and energy principles.

In demonstrating how water can rotate a shaft, water from an 11.0 m high tank (above the shaft) is directed to the turbines of a shaft. Determine the change in gravitational potential energy for 5.0 kg of water.

The force applied to an object moving in the horizontal direction varies with the position, as shown in the figure below. Calculate the work done on the object i) between 0 cm and 2.5 cm, ii) between 2.5 cm and 10 cm, and iii) between 10 cm and 15 cm.  

Sled pulls help athletes develop serious acceleration for sprinting. A sprinter pulls a sled of a mass of 45 kg on a rough horizontal grass surface. The cord makes an angle of 20° with the surface. The coefficient of kinetic friction between the sled and the grass is 0.20. The athlete runs for a distance of 25 m, pulling the cord with a constant force of 120 N. What is the sled's speed at the end of the run? Use the work-energy principle to solve this problem.

The engine of a suspended window cleaning lift moves the platform of mass 125 kg a vertical distance of 65 m. Calculate the work done by the engine. 

A rollercoaster car is released from a height of 50 m and reaches the bottom of the track. What is the velocity of the car at the bottom of the track if it started with an initial velocity of 0 m/s?

An iron ball having a mass of 50 kg is tied to the ceiling using a 2.0 m long chain. Determine the top speed of the iron ball if it is released at an angle of 30 degrees with the vertical.

A 70 kg bobsledder wants to just make it to the top of a 10 m high hill. The track leading up to the hill is a straight path with a length of 50 m. What is the minimum speed the bobsledder needs at the beginning of the track to reach the top of the hill? Assume the track and hill are frictionless.

A ball of 0.5 kg initially at rest is pushed horizontally by a spring with a spring constant of 100 N/m. The spring is compressed by 20 cm before pushing the ball. If the coefficient of kinetic friction is 0.27, what would be the final speed of the ball as it leaves the contact of the spring?

A train starting from rest with a mass of 500,000 kg attains a speed of 30 m/s at a distance of 1500 m. It experiences a thrust of 90 kN from each of its three engines. Calculate the increase in the thermal energy caused by rolling friction.

A skier is skiing in the north direction at 5.0 m/s. The skier experiences a force of 3.0 N from the northwestern winds. The coefficient of kinetic friction is 0 while there exists static friction to prevent the skier from skidding sideways. Determine the skier's speed after skiing 50 m along with the wind. Consider the skier has a mass of 45 kg.

A car with a mass of 1200 kg is travelling at a speed of 25 m/s on an inclined road. It stops at the ground level due to friction after travelling a distance of 150 m. Determine the thermal energy generated by friction during its deceleration. Consider the angle of inclination of the road with the vertical is 70°.

A 3.0 kg box is pushed across a horizontal surface with a speed of 1.5 m/s. The box travels a distance of 1.25 m before coming to a stop. What is the coefficient of kinetic friction between the box and the surface?

A 70 kg skier comes to a stop after skiing down a hill. The kinetic energy she had at the top of the hill is converted into thermal energy by the friction between the skis and the snow. If 4200 J of energy is generated, what was the skier's initial speed at the top of the hill? (Assume all the energy is converted into thermal energy)

Determine the work done by the interaction forces acting between two objects. Consider the change in kinetic energy is 17 J and the change in the potential energy is -9 J.

A bullet is fired vertically with an initial kinetic energy of K₀ J. If it reaches a maximum height of h m, what maximum height will it reach if the bullet's initial kinetic energy is increased by a factor of 4? Consider v₀ as the magnitude of the initial velocity of the bullet.

A 0.75 kg block is attached to a horizontal spring with a spring constant of 400 N/m. The block is pulled towards the right by 8 cm from its equilibrium position and then released. What is the maximum speed of oscillation of the block? Consider the motion in the right direction to be positive. Assume the surface is frictionless.

In a survey conducted on motorbikes, it was found that particular bike tyres could easily absorb 350 J of energy. Determine the maximum height from which a motorbike carrying a man will land safely without failure of its tyres. Consider the combined mass of the man and motorbike as 80 kg.

A labourer is pushing a 3.2 kg box on level ground with a force given by F_x = (18 - 3x) N, where x is in 'm'. Determine the speed of the box when it is pushed to a distance of 5.0 m if the box is initially at rest. Consider that μ_k between the box and the ground is 0.23.

An 86 g ball is catapulted from a slingshot. During its release, the slingshot's elastic band exerts an average force of 106 N on the ball over a distance of 0.76 m. Determine the ball's exit speed.

A 65.5-kg mountaineer begins at an altitude of 1140 m and ascends to a summit of 2650 m above sea level. Can the actual work done by the mountaineer exceed the minimum work required based on the change in gravitational potential energy?

A 65.5-kg climber begins at an altitude of 1140 m and ascends to a summit of 2650 m above sea level. Calculate the least amount of work required by the climber.

Consider a situation in which a scooter travels at a speed of 'v' m/s with a stopping distance of 'd' m. Determine the scooter's revised minimum stopping distance when its velocity is raised to '3v' m/s.

A 78 kg anvil at rest, was dropped from a height of 210 m above the ground. After crashing into the ground, it got buried 1.2 m into the soil. Given that the terminal velocity of the anvil was 52 m/s, calculate how much work the soil did on it to bring it to rest again.

A bungee jumper with mass m falls from a platform that is at height $L$ above a bridge. This setup results in a total fall distance of $2L$ meters before the bungee cord, which has an unstretched length of $L$ and a spring constant $k$, starts to stretch. The cord is designed to ensure the jumper's safety by decelerating the fall. Determine the maximum extension $y$ of the bungee cord using the jumper's mass $m$, the spring constant $k$, and the initial length of the cord $L$ .

A thrill-seeker plans to perform a safe jump off a 30.0-meter-high platform using an elastic rope. The individual has a mass of 70.0 kg and the jump involves a free fall of 60.0 meters in total before the elastic rope, which has an unstretched length of 30.0 meters, begins to stretch to arrest the fall. The rope, with a spring constant of 50.0 N/m, is carefully selected to ensure the jumper is safely brought to a stop without touching the ground. Calculate the maximum extension of the rope during the jump to ensure the safety of the thrill-seeker.

A group of students experimented on objects falling from rest. They dropped a bowling ball of mass 5.2 kg from 110 m above the ground into the sand. After reaching the ground, the bowling ball sank 0.59 m deep into the sand before stopping. If the terminal velocity of the bowling ball was 32 m/s, calculate the average force the sand exerted on it that eventually made it stop.

How much work is needed to move a supply module with mass $m$ from an orbit of radius $2R_E$ to the International Space Station's orbit at $4R_E$, where $R_E$ is Earth's radius?

A student threw a 65-g metal ball horizontally into a soft lump of clay at a velocity of 32 m/s. After traveling a distance of 17 cm into the lump of clay, the ball stopped. Applying the work-energy principle, calculate the average force exerted by the clay onto the metal ball.

Investigators found that a truck's skid mark extended 79 m at the site of a collision on a flat highway. The weather was rainy, and the coefficient of friction was 0.31. Estimate the truck's speed at the moment the brakes were fully applied.

Given that a van leaves a skid mark of 79 m on a flat street in rainy conditions with a friction coefficient of 0.31, why does the mass of the van not influence the skid mark distance?

Given that a bus leaves a skid mark of 79 m on a flat street in rainy conditions with a friction coefficient of 0.31, what issue arises with a bus that skids?

A robot measuring 1.50 m in height raises a 2.50 kg box from ground level to a height of 2.50 m above the ground. Examine how the work done by the robot is related to the potential energies of the box relative to the ground and relative to the top of the robot's head.

An engineer is designing an air-powered cannon to shoot tennis balls. He wants it to shoot the tennis balls at a speed of 32 m/s. Given that the length of the cannon barrel should be 62 cm and the mass of a tennis ball is 58 g, using the work-energy principle, calculate the constant force F that the air pressure should apply on a tennis ball over the length of the barrel.

A 632 kg satellite, at a height of 325 km above the surface, moves at 85.6 m/s vertically down towards Mars. After some time, it hits the surface and rests after penetrating 5.65 m beneath the surface. Ignoring air resistance, calculate the work done by the Martian soil that made the satellite stop.

[Hint: The radius of Mars is 3390 km. The mass of Mars is 6.39 x 10²³ kg. And the gravitational acceleration on Mars is 3.72 m/s².]

A meteor with a mass of 2.0$\times$10⁴ kg is approaching Earth. It is currently 1.5$\times$10⁶ m away and moving directly towards the Earth with a velocity of 200 m/s. If no external forces act upon it, what will be its speed upon impact with the Earth's surface?

Hint: gravitational constant G = 6.67$\times$10^-11 Nm²/kg²

mass of earth M_E = 5.98$\times$10²⁴ kg

radius of earth r_E = 6.38$\times$10⁶ m

Seismic isolators, used in earthquake-prone areas, consist of springs supporting a heavy base to dampen ground vibrations. Picture an isolator with a spring (mass $M_S$, natural length $L$) and a heavy base (mass $m$) designed for horizontal, frictionless movement. The spring's design ensures that the movement speed at each point is proportional to its distance from the fixed end during seismic activities. Determine the expression for the kinetic energy ($KE$) of this system when the base moves at speed $v$.

A small ball of mass 2.3 kg was initially moving with a velocity v̄₀ = (11.0 î + 31.0 ĵ) m/s. Afterward, a force F̄ acted on it for 3.0 s. As a result, its final velocity became v̄_f = (20.0 î + 35.0 ĵ) m/s. Calculate the work done on the ball by the force F̄.

A metal sheet with a mass of 3.0 kg is being pushed over the floor of a factory (Fig. 1). The floor offers a steady resistance to motion, known as kinetic friction, with a coefficient of 0.35. At the beginning, the sheet is at the position marked as x = 0.0 and it's moving at a speed of 2.0 m/s. The force used to push the sheet is angled 15° below the horizontal, and this force grows stronger the farther the sheet moves, which is illustrated in Fig. 2. Draw a line on the graph showing the magnitude of the friction force versus distance x.