A person is pushing on a refrigerator that sits on a level floor. Use Newton's third law along with his second law to find the magnitude of the acceleration of a man as he pushes the refrigerator. Assume the man has a mass of 62 kg, he exerts a force of 128 N, the refrigerator has a mass of 187 kg, and the floor is very slippery so that there is no frictional force between the floor and the man.

F = m a is the equation you use

It's called Newton's second law.

The equation applies bioth to to the man and the refrigerator, but the accelertions of the two are different, since the masses ara different

You want to know the acceleration of the man, a.
So m must be the man's mass, 62 kg
F is the force exerted by the refrigerator on the man, which is -128 N

The minus sign is there if the positive direction is that of the man's force on the refrigerator. The force on the man is equal and opposite. The man accelerates backwards. That is where Newton's Third law is used.

a = -128 N/62 kg = -2.06 m/s^2

To find the magnitude of the acceleration of the man as he pushes the refrigerator, we can first calculate the net force acting on the man-refrigerator system using Newton's second law.

Newton's second law states that the net force (F_net) acting on an object is equal to the product of its mass (m) and acceleration (a). Mathematically, this can be represented as:

F_net = m * a

Let's calculate the net force acting on the man-refrigerator system:

Total mass of the system (m_total) = mass of the man + mass of the refrigerator
m_total = 62 kg + 187 kg
m_total = 249 kg

Net force (F_net) = 128 N (force exerted by the man)

Now, using Newton's third law, we know that the force exerted by the man on the refrigerator is equal in magnitude and opposite in direction to the force exerted by the refrigerator on the man. Therefore, the net force can be considered as the force exerted by the man minus the force exerted by the refrigerator:

F_net = Force exerted by the man - Force exerted by the refrigerator

Since there is no friction between the man and the floor, the only force opposing the man's push is the force exerted by the refrigerator. Therefore:

F_net = Force exerted by the man - Force exerted by the refrigerator
F_net = 128 N - Force exerted by the refrigerator

Now, we can set up an equation using Newton's second law and solve for the acceleration (a):

F_net = m_total * a
128 N - Force exerted by the refrigerator = 249 kg * a

To continue solving this problem, we need the magnitude of the force exerted by the refrigerator. The given information does not provide this value, so we cannot calculate the specific magnitude of the acceleration without that information.

To find the magnitude of acceleration of the man as he pushes the refrigerator, we can follow these steps using Newton's laws:

Step 1: Identify the forces involved:

- Force exerted by the man on the refrigerator (F_man-ref): 128 N
- Mass of the man (m_man): 62 kg
- Mass of the refrigerator (m_ref): 187 kg

Step 2: Apply Newton's second law:

According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration.

The net force acting on the man-refrigerator system is the force exerted by the man (F_man-ref) minus the force exerted by the refrigerator on the man (F_ref-man):

Net force (F_net) = F_man-ref - F_ref-man

Since we know that the force between the man and the refrigerator (F_man-ref) has the same magnitude but opposite direction to the force between the refrigerator and the man (F_ref-man), we can conclude that F_man-ref = -F_ref-man. Therefore, the net force acting on the system is:

F_net = F_man-ref - (-F_man-ref) = F_man-ref + F_man-ref = 2F_man-ref

Step 3: Calculate the acceleration:

Since F_net = ma (where a is the acceleration), we can write the equation as:

2F_man-ref = (m_man + m_ref) * a

Plugging in the given values:

2 * 128 N = (62 kg + 187 kg) * a

Simplifying the equation:

256 N = 249 kg * a

Dividing both sides by 249 kg:

a = 256 N / 249 kg

Calculating the numerical value:

a ≈ 1.0281 m/s²

Therefore, the magnitude of the acceleration of the man as he pushes the refrigerator is approximately 1.0281 m/s².