A 6.0-kg box moving at 3.0 m/s on a horizontal, friction-less surface runs into a light spring of force constant 75 N/cm. Use the work—energy theorem to find the maximum compression of the spring.

The maximum compression in the spring is 0.085 m or 8.5 cm.

Explanation:

Given:

Mass of box (m) = 6.0 kg

Spring constant of spring (k) = 75 N/cm = 75 × 100 N/m = 7500 N/m

Initial velocity of the box (u) = 3.0 m/s

Final velocity at maximum compression (v) = 0 m/s

Let the maximum compression be 'x'.

Surface is frictionless. So, only spring force is the force acting on the box spring system.

Now, as per work-energy theorem, the work done by the net force acting on a body is equal to the change in the kinetic energy of the body.

Here, the work done by the spring force is given as:

The negative sign implies that force and displacement are in opposite direction.

The change in kinetic energy is given as:

Now, from work-energy theorem:

Now, plug in the given values and solve for 'x'. This gives,

Therefore, the maximum compression in the spring is 0.085 m or 8.5 cm.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.