The force that translates to the entire system is that of gravity acting on the mass hanging over the ledge.



140N is the total force acting on the system, which has a mass equal to both blocks combined (65 kg + 14 kg = 79 kg). We can find the acceleration using Newton's second law.

Newton’s second law can be used in combination with the spring force equation to solve for the acceleration of the system. Remember that any force, whether it is kinematic, electrical, or gravitational, is equal to Newton’s second law. 

F_spring = kx = ma_system

If the rope can only withstand 800N of force, we can solve for the mass of the object which would result in this maximum force when hanging from the rope.

The equation for force is  This shows that by increasing the man's mass, his force will increase after jumping from the plane.

All other options will result in a decreased acceleration when falling. Falling with his stomach downward increases the surface area of the diver, which increases his air resistance. A parachute will also increase the air resistance and surface area. If the plane is descending when he jumps, his time to reach terminal velocity will be reduced, as he will already have an initial velocity in the downward direction.

To solve this problem use Newton's second law:

We are given the acceleration and the force, both in the horizontal direction. Using these values we can find the mass of the jet.

An elevator car with its counterweight is a crude example of an Atwood machine, the device described in this question. The acceleration in an Atwood machine varies between zero (the masses are equal) and the full value of gravitational acceleration (one mass is very near zero and the other is very large).

Here, the total mass being accelerated is the sum of the two, or 0.3 kg, so the trick is to find the net force acting on the masses. Although the formal presentation in physics texts looks daunting, just consider that one mass is attempting to fall by pulling up on the other mass, and vice versa. Each experiences a downward force due to gravity:

This force is transmitted through the string to an upward force on the opposite mass. The net force is simply the gravitational force acting on one mass minus that acting on the other:

Now that we know the net force and the total mass, we can determine the acceleration using Newton's second law:

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You can easily substitute in numbers to see why the Atwood machine has possible solutions between  and . If both masses were , obviously the net force would be zero, and so would the acceleration. If one mass was  and the other was , the acceleration would be , almost equal to gravitational acceleration.

The force in the string is all generated by the suspended mass. This value will be equal to the gravitational force acting on the suspended mass.

Using this force, we can determine the acceleration on the total mass of the system. The total mass being accelerated is:

Use Newton's second law to calculate the acceleration of the system.

Note that the net force and acceleration are negative, indicating that the net movement will be in the downward direction.

It is important to understand that even if the block cannot provide a frictional force to resist being pulled to the right, it still has to be accelerated; Newton's second law is obeyed in frictionless and gravity-free situations (like outer space). This issue is well demonstrated with an Atwood machine.

First, find the net force by subtracting the opposing forces.

F = 1020N – 175N = 845 N to the west

Next, find acceleration using Newton's second law, .

The only force acting on the ball at any point during flight is the downwards force of gravity, which is constant. There are no forces acting on the ball in the horizontal direction. Any acceleration will result in a force, according to Newton's second law.

If there are no other forces, then we can assume that there are no other accelerations acting on the ball. Acceleration due to gravity is constant. If this is the only acceleration on the ball, then the acceleration must be constant throughout flight.

Solve the following equation for acceleration, using the values given in the question.