In Figure P4.30, m1 = 10.5 kg and m2 = 4.5 kg. The coefficient of static friction between m1 and the horizontal surface is 0.60 while the coefficient of kinetic friction is 0.30.

Figure P4.30

To answer this question, we need to understand how to calculate the force of friction. The force of friction can be calculated using the formula:

f = μ * N

where f is the force of friction, μ is the coefficient of friction, and N is the normal force.

First, let's calculate the normal force (N) for both m1 and m2. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of each object.

For m1, the weight is given by the formula:

Weight = mass * gravity

where mass is 10.5 kg and gravity is approximately 9.8 m/s^2.

Weight of m1 = 10.5 kg * 9.8 m/s^2 = 102.9 N

Therefore, the normal force (N) acting on m1 is 102.9 N.

Similarly, for m2, the weight is given by the formula:

Weight = mass * gravity

where mass is 4.5 kg and gravity is approximately 9.8 m/s^2.

Weight of m2 = 4.5 kg * 9.8 m/s^2 = 44.1 N

Therefore, the normal force (N) acting on m2 is 44.1 N.

Now, let's calculate the force of friction (f) for both cases: static and kinetic.

For static friction (fs), the formula is:

fs = μs * N

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

fs = 0.60 * 102.9 N = 61.74 N

Therefore, the force of static friction (fs) is 61.74 N.

For kinetic friction (fk), the formula is:

fk = μk * N

where μk is the coefficient of kinetic friction and N is the normal force.

fk = 0.30 * 102.9 N = 30.87 N

Therefore, the force of kinetic friction (fk) is 30.87 N.

Remember to always double-check the units used in the problem and use consistent units throughout the calculations.

4.2