4.57 Your refrigerator has a mass of \(112.2 \mathrm{~kg}\), including the food in it. It is standing in the middle of your kitchen, and you need to move it. The coefficients of static and kinetic friction between the fridge and the tile floor are 0.460 and 0.370 , respectively. What is the magnitude of the force of friction acting on the fridge, if you push against it horizontally with a force of each magnitude? a) \(300 \mathrm{~N}\) b) \(500 \mathrm{~N}\) c) \(700 \mathrm{~N}\)

To calculate the normal force, multiply the mass of the refrigerator by the acceleration due to gravity (approximately \(9.8 \mathrm{m/s^2}\)). \(N = m \times g = 112.2 \mathrm{~kg} \times 9.8 \mathrm{m/s^2} = 1099.16 \mathrm{~N}\)

Use the static friction coefficient (0.460) and the normal force calculated in Step 1 to find the maximum force of static friction. \(F_{s_{max}} = \mu_s * N = 0.460 * 1099.16 \mathrm{~N} = 505.21 \mathrm{~N}\) Now let's calculate the kinetic friction (\(F_k\)) for when the refrigerator is moving: \(F_k = \mu_k * N\) Where \(\mu_k\) is the kinetic friction coefficient.

Use the kinetic friction coefficient (0.370) and the normal force calculated in Step 1 to find the kinetic friction. \(F_k = \mu_k * N = 0.370 \times 1099.16 \mathrm{~N} = 406.69 \mathrm{~N}\) Now that we have the maximum force of static friction and the kinetic friction, we can find the force of friction for each applied force magnitude. Remember to check if the applied force is greater than the maximum force of static friction (if yes, the refrigerator will move and we should use \(F_k\), otherwise we use applied force when the refrigerator doesn't move).

a) For an applied force of \(300 \mathrm{~N}\), Since \(300 \mathrm{~N} < F_{s_{max}}\), the refrigerator doesn't move, so the force of friction is equal to the applied force. Force of friction = \(300 \mathrm{~N}\) b) For an applied force of \(500 \mathrm{~N}\), Since \(500 \mathrm{~N} < F_{s_{max}}\), the refrigerator doesn't move, so the force of friction is equal to the applied force. Force of friction = \(500 \mathrm{~N}\) c) For an applied force of \(700 \mathrm{~N}\), Since \(700 \mathrm{~N} > F_{s_{max}}\), the refrigerator moves, so the force of friction is equal to the kinetic friction. Force of friction = \(406.69 \mathrm{~N}\) Hence, the magnitudes of the force of friction for each applied force are: a) \(300 \mathrm{~N}\) b) \(500 \mathrm{~N}\) c) \(406.69 \mathrm{~N}\)