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 20 kg crate is being pulled up a 20° incline with a constant velocity by a force F at an angle of 15° below the horizontal. Determine the work done by the weight (mg), normal force (F_N) and applied force (F) on the crate as it travels 10 m along the incline.

Consider the hill depicted in the figure below was not an even slope but an irregularly shaped curve. Suppose a sled is pulled up the hill. The work done by gravity will depend upon which parameters?

A specialist has purchased repair material to fix a torn canvas. However, they cannot trace the documentation of the material. They pick a technique to experimentally test the elastic properties of the material. They cut out a 25.0 cm piece of the material and apply a pull of 2.40 N on it. They observe the material to stretch by 2.20 cm. Calculate the force constant of the material.

Stretching a rubber band 4.0 cm from its equilibrium length requires 8.0 J of energy. What extra work is needed in order to stretch the rubber band an additional 2.0 cm?

A tennis ball launcher uses a spring mechanism to project balls. The force to compress the spring an amount $z$ is given by $F = 100z + 5z^3$ , where $z$ is in meters and $F$ in newtons. If the spring is compressed 0.80 m, what speed will it give to a 0.057-kg tennis ball when released?

A motor pulls a 255 kg cart filled with crushed stone up rail bars inclined at 30 degrees at a uniform speed of 200 cm/s. The kinetic friction coefficient between the cart and the rail bars is 0.25. Determine the power output of the motor.

Food containers are commonly made of aluminum. A 20 kg aluminum food crate slides against an aluminum table that has a kinetic coefficient of friction, μ_k = 0.46. A worker pushes the crate at a uniform speed of 0.80 m/s for 5s. Determine the worker's power output.

On a flat horizontal highway, a 350 kg motorcycle's speed drops from 86 km/h to 70 km/h in 5.0 s while it is in neutral gear. Calculate what the approximate value of power (both in watts and hp) that will be needed for the motorcycle to maintain a constant speed of 72 km/h on the highway.