Energy A shopping velocity of the 28-kg cartoon release is 3.5m/s and it stop. It's distance of 6.0 meters betwer stopping, determine the magnitude of the friction on the before then the kinetic energy stays the SEP Use Mathematics

To determine the magnitude of the friction force acting on the shopping cart, we can use the work-energy principle. The work done by the friction force will be equal to the change in kinetic energy of the cart.<br /><br />Given information:<br />- Mass of the shopping cart, m = 28 kg<br />- Initial velocity of the cart, v_initial = 3.5 m/s<br />- Final velocity of the cart, v_final = 0 m/s (since it stops)<br />- Distance traveled before stopping, d = 6.0 m<br /><br />Step 1: Calculate the initial kinetic energy of the cart.<br />Kinetic energy, KE = (1/2) * m * v^2<br />KE_initial = (1/2) * 28 kg * (3.5 m/s)^2<br />KE_initial = 196.25 J<br /><br />Step 2: Calculate the final kinetic energy of the cart.<br />KE_final = (1/2) * m * v_final^2<br />KE_final = (1/2) * 28 kg * (0 m/s)^2<br />KE_final = 0 J<br /><br />Step 3: Calculate the change in kinetic energy.<br />ΔKE = KE_final - KE_initial<br />ΔKE = 0 J - 196.25 J<br />ΔKE = -196.25 J<br /><br />Step 4: Calculate the work done by the friction force.<br />Work done by friction, W_friction = -ΔKE<br />W_friction = -(-196.25 J)<br />W_friction = 196.25 J<br /><br />Step 5: Calculate the magnitude of the friction force.<br />Work done by friction, W_friction = F_friction * d<br />F_friction = W_friction / d<br />F_friction = 196.25 J / 6.0 m<br />F_friction = 32.54 N<br /><br />Therefore, the magnitude of the friction force acting on the shopping cart is 32.54 N.