a 64.5 person steps off a 129 kg boat with a force of 34.0 N. which object will have the larger acceleration?
To determine which object will have the larger acceleration, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation for this is:
a = F / m
where:
a represents acceleration,
F represents the net force acting on the object, and
m represents the mass of the object.
Let's calculate the acceleration for both the person and the boat.
For the person:
Given:
F_person = 34.0 N (force exerted by the person on the boat)
m_person = 64.5 kg (mass of the person)
Using the equation a = F / m, we can substitute the values to find the acceleration:
a_person = F_person / m_person
= 34.0 N / 64.5 kg
= 0.527 acceleration
For the boat:
Given:
F_boat = -F_person (according to Newton's third law, the force exerted by the person on the boat is equal in magnitude but opposite in direction to the force exerted by the boat on the person)
m_boat = 129 kg (mass of the boat)
Using the equation a = F / m, we can substitute the values to find the acceleration:
a_boat = F_boat / m_boat
= -F_person / 129 kg (since force is in the opposite direction)
= -34.0 N / 129 kg
= -0.264 acceleration
Comparing the two values, we find that the person has an acceleration of 0.527 m/s^2, while the boat has an acceleration of -0.264 m/s^2.
Therefore, the person will have the larger acceleration since their acceleration is positive and greater in magnitude than the acceleration of the boat.