A person in a kayak starts paddling, and it accelerates from 0 to 0.59 m/s in a distance of 0.43 m. If the combined mass of the person and the kayak is 72 kg, what is the magnitude of the net force acting on the kayak?
V^2 = Vo^2 + 2a*d
a = (V*2-Vo^2)/2d
a = (0.59^2-0)/0.86 = 0.405 m/s^2.
Fn = m*a = 72 * 0.405 = 29.1 N.
To find the magnitude of the net force acting on the kayak, we can use Newton's second law of motion, which states that the net force is equal to the product of the mass and acceleration:
Net force (F) = mass (m) × acceleration (a)
In this case, the mass of the person and the kayak combined is given as 72 kg. The acceleration can be determined using the formula:
Acceleration (a) = (final velocity - initial velocity) / distance
From the information given, the initial velocity is 0 m/s (since the kayak starts from rest), the final velocity is 0.59 m/s, and the distance covered is 0.43 m.
Substituting these values into the formula, we have:
Acceleration (a) = (0.59 m/s - 0 m/s) / 0.43 m
Simplifying, we get:
Acceleration (a) = 0.59 m/s / 0.43 m
Acceleration (a) ≈ 1.37 m/s²
Now, we can substitute the mass (m) and acceleration (a) values into the formula for net force:
Net force (F) = 72 kg × 1.37 m/s²
Calculating this, we have:
Net force (F) ≈ 98.64 N
Therefore, the magnitude of the net force acting on the kayak is approximately 98.64 Newtons.