Question

an ice skater applies a horizontal force to a 20 kg block on frictionless, level ice causing the block to accelerate uniformly at 1.4 m/s^2 to the right. after the skater stops pushing the block it slides onto a region of ice that is covered with a thin layer of sand. the coefficient of kinetic friction between the block and the sand-covered ice is 0.28 calculate the magnitude of the normal force applied to the block

Answer 1

To calculate the magnitude of the normal force acting on the block, we need to consider the forces acting on it in the vertical direction.

1. Weight of the block: The weight (\(W\)) of the block can be calculated using the formula: \[ W = m \cdot g \] where:

   • \(m = 20 , \text{kg}\) (mass of the block)
   • \(g = 9.81 , \text{m/s}^2\) (acceleration due to gravity)

   Substituting the values: \[ W = 20 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 196.2 , \text{N} \]

2. Normal force (\(N\)): On frictionless surfaces, the normal force typically balances the weight of the object. Therefore, if the ice is level and there are no vertical forces acting other than weight and the normal force, we have: \[ N = W = 196.2 , \text{N} \]

Thus, the magnitude of the normal force applied to the block is 196.2 N.