Final answer:
Dominique and Blake can determine the force of kinetic friction by calculating the work done through the formula f_k = μ_k N, using the mass of the object, coefficient of kinetic friction, and measuring the distance the object moves after being impacted by a marble.
Step-by-step explanation:
To determine the force of kinetic friction exerted on a wooden piece, Dominique and Blake need to calculate the work done by friction and the distance the object moves. Since kinetic friction is constant while the object is in motion, the work done by friction (Wfr) can be calculated by multiplying the kinetic friction force (f(k)) by distance (d).
The force of kinetic friction is given by f(k) = μk N, where μk is the coefficient of kinetic friction and N is the normal force. The normal force is usually the weight of the object, which is mass (m) times the acceleration due to gravity (g). If Dominique and Blake know the mass of the wooden piece and the coefficient of kinetic friction between the wood and the surface, they can easily compute the force of kinetic friction using these variables.
Additionally, if they perform an experiment where a marble hits the wooden piece and causes it to move, they can measure the distance the piece moves to calculate the work done by friction. They can then use this to back-calculate the kinetic friction force. If they conduct multiple experiments varying the mass of the marbles, they can investigate if the distance moved is proportional to the mass, which will provide them further insights into the relationship between kinetic energy and work done by friction.