Final answer:
The frictional force on a block will match the external force up to the maximum static friction limit and is always directed opposite to the external force. For external forces of 0 N, 4.9 N, and 9.8 N, the frictional forces will be 0 N, 4.9 N, and 9.8 N, respectively, all to the left.
Step-by-step explanation:
To determine the magnitude and direction of the force of friction on a block on a horizontal surface given different magnitudes of an external horizontal force, we must consider the coefficient of static friction and the normal force acting on the block. The gravitational force acting on the block equals the normal force as long as the block is on a horizontal surface and there are no other vertical forces. The coefficient of static friction (μs) for the block and the surface in this case is 0.5, and the normal force (N) is equivalent to the weight of the block, which is mass (m) times the acceleration due to gravity (g), giving us N = m × g = 1.2 kg × 9.8 m/s² = 11.76 N.
Now, let's calculate the maximum static friction force, which is f_s(max) = μs × N = 0.5 × 11.76 N = 5.88 N. The static friction will adjust itself to match the external force up to its maximum value. So:
- (a) When the external force is 0 N, the frictional force is also 0 N because there is no need for friction to act when there is no external force.
- (b) When the external force is 4.9 N, which is less than the maximum static friction force, the frictional force will be equal but opposite in direction to the applied force, so the frictional force will be 4.9 N to the left.
- (c) When the external force is 9.8 N, which is still less than the maximum static friction force, the frictional force will also be 9.8 N to the left.
The direction of friction is always opposite to the applied external force, as long as the block is not moving.