Final answer:
a. The work done on the canoe can be calculated using the work-energy principle. Use the formula W = F * d * cosθ, where W is the work, F is the force applied, d is the distance moved, and θ is the angle between the force and the direction of motion. b. The work done by friction on the canoe can be calculated using the equation W = F_friction * d_friction * cosθ, where W is the work, F_friction is the force of friction, d_friction is the distance moved against friction, and θ is the angle between the friction force and the direction of motion. c. The total work performed on the canoe is the sum of the work done on the canoe and the work done by friction on the canoe. d. The force applied to the canoe can be calculated using the equation F = m * a, where F is the force applied, m is the mass of the canoe, and a is the acceleration of the canoe.
Step-by-step explanation:
a. To calculate the work done on the canoe, you can use the work-energy principle which states that work done is equal to the change in kinetic energy. The formula for work is W = F * d * cosθ, where W is the work, F is the force applied, d is the distance moved, and θ is the angle between the force and the direction of motion. In this case, the force applied is equal to the mass of the canoe multiplied by its acceleration, which can be calculated using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. So, the work done on the canoe is W = (14 kg) * [(2.1 m/s)^2 - 0^2] / (2 * 5 m * cos 0°). Solve the equation to find the work done on the canoe.
b. To calculate the work done by friction on the canoe, you can use the equation W = F_friction * d_friction * cosθ, where W is the work, F_friction is the force of friction, d_friction is the distance moved against friction, and θ is the angle between the friction force and the direction of motion. The force of friction can be calculated using the equation F_friction = μ * F_N, where μ is the coefficient of friction and F_N is the normal force. In this case, the normal force is equal to the weight of the canoe, which can be calculated using the formula F_N = m * g, where m is the mass of the canoe and g is the acceleration due to gravity. So, the work done by friction on the canoe is W = (0.2) * [(14 kg) * (9.8 m/s^2)] * (8 m) * cos 180°. Solve the equation to find the work done by friction on the canoe.
c. The work performed on the canoe can be calculated by adding the work done on the canoe to the work done by friction on the canoe. So, the total work performed on the canoe is the sum of the work done on the canoe and the work done by friction on the canoe.
d. The force applied to the canoe can be calculated using the equation F = m * a, where F is the force applied, m is the mass of the canoe, and a is the acceleration of the canoe. In this case, the acceleration can be calculated using the equation a = (v^2 - u^2) / (2 * d), where v is the final velocity, u is the initial velocity, and d is the distance. So, the force applied to the canoe is F = (14 kg) * [(2.1 m/s)^2 - 0^2] / (2 * 5 m). Solve the equation to find the force applied to the canoe.