8. A girl pushes a light (m=0) snow shovel at a uniform velocity across a sidewalk . If the handle of the shovel is inclined at 55^circ to the horizontal , and she pushes along the handle with a force of 100 N, a) What is the force of friction? b) What is the coefficient of kinetic friction?

**a) Force of Friction:**<br /><br />Since the snow shovel is moving at a uniform velocity, the net force acting on it is zero. This means the force applied by the girl along the handle is balanced by the force of friction opposing the motion. However, we need to consider only the horizontal component of the applied force, as that's the component contributing to the shovel's horizontal motion.<br /><br />* **Horizontal component of the applied force:** F_horizontal = F_applied * cos(θ) = 100 N * cos(55°) ≈ 57.36 N<br /><br />Since the net horizontal force is zero, the force of friction must be equal in magnitude and opposite in direction to the horizontal component of the applied force.<br /><br />Therefore, the force of friction is approximately **57.36 N**.<br /><br /><br />**b) Coefficient of Kinetic Friction:**<br /><br />The force of kinetic friction (F_friction) is related to the normal force (F_N) and the coefficient of kinetic friction (μ_k) by the following equation:<br /><br />F_friction = μ_k * F_N<br /><br />To find the normal force, we need to consider the vertical forces acting on the shovel. These are the vertical component of the applied force (acting downwards) and the weight of the shovel (acting downwards), balanced by the normal force (acting upwards). Since the shovel is light (m=0), its weight is zero. Therefore:<br /><br />* **Vertical component of the applied force:** F_vertical = F_applied * sin(θ) = 100 N * sin(55°) ≈ 81.92 N<br />* **Weight of the shovel:** 0 N (since mass is 0)<br /><br />Since the shovel isn't accelerating vertically, the normal force must equal the vertical component of the applied force:<br /><br />F_N = F_vertical ≈ 81.92 N<br /><br />Now we can solve for the coefficient of kinetic friction:<br /><br />μ_k = F_friction / F_N ≈ 57.36 N / 81.92 N ≈ **0.7**<br /><br />Therefore, the coefficient of kinetic friction is approximately **0.7**.<br />