A 15 kg box slides across the floor with an initial velocity of +7.6 m/s. It comes to a stop after sliding +14.8 m.

How much friction was present?

To determine the amount of friction that was present, we can use the principle of conservation of energy and apply the work-energy theorem.

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the box is the work done by friction, which causes the box to come to a stop.

The equation for the work done by friction is given by:

Work = Force x Distance

In this case, the work done by friction is equal to the force of friction multiplied by the distance the box slides. When the box comes to a stop, all of its kinetic energy is converted into work done by friction.

The equation for the work-energy theorem can be written as:

Work = Change in Kinetic Energy

The change in kinetic energy can be calculated using the initial velocity, final velocity, and mass of the box. The initial kinetic energy is given by:

Kinetic Energy_initial = (1/2) * mass * (initial velocity)^2

The final kinetic energy is zero since the box comes to a stop, so:

Kinetic Energy_final = 0

Therefore, the change in kinetic energy is:

Change in Kinetic Energy = Kinetic Energy_final - Kinetic Energy_initial
= 0 - ((1/2) * mass * (initial velocity)^2)

Now, equating the work done by friction to the change in kinetic energy, we have:

Force of Friction x Distance = -((1/2) * mass * (initial velocity)^2)

The force of friction can be found by dividing both sides of the equation by distance:

Force of Friction = -((1/2) * mass * (initial velocity)^2) / distance

Plugging in the values, we have:

Force of Friction = -((1/2) * 15 kg * (7.6 m/s)^2) / 14.8 m
= -((1/2) * 15 kg * 57.76 m^2/s^2) / 14.8 m

Simplifying the equation, we get:

Force of Friction = -441.6 N / 14.8 m
= -29.84 N

Therefore, the amount of friction present is approximately 29.84 N. Note that the negative sign indicates that the friction is acting in the opposite direction to the initial motion of the box.