Question

A block of mass 14.2 kg is sliding at an initial velocity of 6.15 m/s in the positive x-direction. the surface has a coefficient of kinetic friction of 0.153. (indicate the direction with the signs of your answers.) hint

Answer 1

The acceleration of the block is approximately -2.06 m/s^2 in the negative x-direction.

Step-by-step explanation:

To find the acceleration of the block, we need to consider the forces acting on it. In this case, the only horizontal force is the frictional force, which opposes the motion. The frictional force can be calculated using the coefficient of kinetic friction and the normal force. The normal force is equal to the weight of the block, which is given by the mass times the acceleration due to gravity. Using this information, we can calculate the acceleration using Newton's second law, which states that the net force is equal to the mass of an object multiplied by its acceleration.

Using the formula:

F_friction = coefficient of kinetic friction * normal force

where normal force = mass * acceleration due to gravity

we can substitute the values:

F_friction = 0.153 * (14.2 kg * 9.8 m/s^2)
Then, we can calculate the net force:

net force = F_friction

Now we can use Newton's second law:

net force = mass * acceleration

Substituting the values, we get:

0.153 * (14.2 kg * 9.8 m/s^2) = 14.2 kg * acceleration

Simplifying the equation, we find that the acceleration of the block is approximately -2.06 m/s^2 in the negative x-direction.