A block whose weight is 34.0 N rests on a horizontal table. A horizontal force of 27.2 N is applied to the block. The coefficients of static and kinetic friction are 0.600 and 0.472, respectively. Will the block move under the influence of the force, and, if so, what will be the block's acceleration? If the block does not move, give 0 m/s2 as the acceleration.

Fap - 0.6*34 = m*a = m*0 = 0

Fap = 20.4N,mln. = Force applied.
27,2 N will move the block.

m*g = 34
m*9.8 = 34
m = 3.47 kg

a=Fn/m = (27.2-0.472*34)/3.47=3.21 m/s^2

To determine whether the block will move or not, we need to compare the force applied to the block with the maximum force of static friction that can be exerted on the block. The maximum force of static friction can be calculated using the formula:

Static Friction = coefficient of static friction * Normal force

Where the Normal force is the force exerted by the table on the block, which is equal to the weight of the block (34.0 N) in this case.

Static Friction = 0.600 * 34.0 N = 20.4 N

Since the applied force (27.2 N) is larger than the maximum force of static friction (20.4 N), the block will start to move.

The block's acceleration can be determined using Newton's second law of motion:

Net Force = mass * acceleration

In this case, the net force is the difference between the applied force and the force of kinetic friction, which is given by:

Kinetic Friction = coefficient of kinetic friction * Normal force

Kinetic Friction = 0.472 * 34.0 N = 16.048 N

Net Force = Applied Force - Kinetic Friction
= 27.2 N - 16.048 N
= 11.152 N

Now, solving for acceleration:

11.152 N = mass * acceleration

To find the acceleration, we need to know the mass of the block. If the mass is given, you can substitute it in the equation and solve for acceleration by dividing both sides of the equation by the mass.