A 0.40 kg block rests on a desk. The coefficient of static friction is 0.20. You push the side of the block but do not have a spring scale to measure the force you use. The block does not move. Which statement is true about the force of static friction?

It is no larger than 0.78 N.

It is 0.08 N.

It is 0.78 N.

It is no smaller than 0.78 N.

Well, it seems like this situation is quite the puzzle! The force of static friction is determined by the coefficient of static friction and the normal force acting on the block. In this case, since the block is not moving, the force of static friction must be equal and opposite to the force you are applying. So, if you keep pushing with all your might (or maybe with all your clown-sized might), the force of static friction must be no smaller than 0.78 N. So, the statement "It is no smaller than 0.78 N" is true. Keep pushing, my friend!

The statement "It is no larger than 0.78 N" is true about the force of static friction in this situation.

The force of static friction can be calculated using the equation:

f_s = μ_s * N

where f_s is the force of static friction, μ_s is the coefficient of static friction, and N is the normal force.

In this case, the coefficient of static friction is given as 0.20. The normal force is equal to the weight of the block, which can be calculated using:

N = m * g

where m is the mass of the block and g is the acceleration due to gravity.

Given that the mass of the block is 0.40 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the normal force:

N = 0.40 kg * 9.8 m/s^2 = 3.92 N

Using this value for the normal force and the coefficient of static friction, we can calculate the maximum force of static friction:

f_s = 0.20 * 3.92 N = 0.784 N

Therefore, the force of static friction is no larger than 0.78 N.

To determine the force of static friction acting on the block, we can use the equation:

fs = μs * N

where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.

The normal force N is equal to the weight of the block, which can be calculated by multiplying the mass of the block (0.40 kg) by the acceleration due to gravity (9.8 m/s^2):

N = m * g
N = 0.40 kg * 9.8 m/s^2
N = 3.92 N

Substituting the values into the equation for static friction:

fs = 0.20 * 3.92 N
fs = 0.784 N

Therefore, the force of static friction acting on the block is 0.784 N.

The statement "It is no larger than 0.78 N" is incorrect because the force of static friction is exactly 0.784 N, which is larger than 0.78 N.

The statement "It is 0.08 N" is incorrect because 0.08 N is not equal to the force of static friction.

The statement "It is no smaller than 0.78 N" is incorrect because the force of static friction is not larger than 0.784 N.

The correct statement is "It is 0.78 N," as the force of static friction is exactly that value.

maximum friction force = mu m g

= .2 * .4 * 9.81 = .787 Newtons

so it is less than or equal to .787 Newtons (or .78 N if you use 9.8 for g and round to two significant figures)