A 48.2 kg girl is standing on a 160. kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 2.00 m/s to the right relative to the plank.
(a) What is her velocity relative to the surface of the ice?
To find the girl's velocity relative to the surface of the ice, we need to consider the forces acting on the plank-girl system.
Since the plank is on a frictionless surface, there is no force opposing the motion of the system along the surface of the ice. This means that the net force in the horizontal direction is zero.
The only horizontal force acting on the system is the force of friction between the girl's feet and the plank. This force opposes the motion of the girl relative to the plank. However, we are told that the girl walks at a constant velocity of 2.00 m/s to the right relative to the plank. This means that the force of friction must be equal in magnitude and opposite in direction to the force exerted by the girl, making the net force zero.
Since the net force is zero, the acceleration of the system is also zero. According to Newton's second law (F = ma), if the net force is zero, the product of mass and acceleration is also zero.
The total mass of the system is the sum of the girl's mass and the mass of the plank, which gives us 48.2 kg + 160 kg = 208.2 kg.
Therefore, the acceleration of the system is zero, and the girl's velocity relative to the surface of the ice is also 2.00 m/s to the right.