Balance and Force

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Dynamics: unbalanced forces

Newton's 2nd Law

​F = ma

In equilibrium, a = 0, thus all forces are balanced.

If the system is accelerating, then the forces are unbalanced and the net sum of the forces = mass x acceleration.

Math Response

don't use units...

Type answer here

Correct Answer: 77

Deg^°

Rad

Math Response

Remember tension is force

Type answer here

Correct Answer: 1450

Deg^°

Rad

Math Response

Use kinematics to find the acceleration.

Then F = ma

Type answer here

Correct Answer: 211

Deg^°

Rad

Multiple Choice

How would you describe the vertical direction forces in this free body diagram?

• Balanced

• Unbalanced

Multiple Choice

What is the horizontal net force acting on this object?

• 35 N

• 50 N

• -5 N

• 5 N

Multiple Choice

What is the net force in the vertical direction?

• 0 N

• 50 N

• -25 N

• 25 N

Multiple Choice

What is the acceleration of this object if it has a mass of 10 kg?

• 1.6 m/s²

• 9.8 m/s2

• 5 m/s²

• 0.5 m/s²_

Multiple Choice

A box has three forces applied to it in the horizontal direction: a 50 N force to the right, a 30 N force to the left & a 20 N force to the right. What is the net force on the box?

• 40 N to the left

• 40 N to the right

• 100 N to the right

• 100 N to the left

Multiple Choice

The free body diagram of four boxes are shown below. Which box is in equilibrium?

Elevator Problems and weight

WEIGHT is the NORMAL Force

In equilibrium, we like to say that weight is mg.

If the system is accelerating, though the weight of the object is now different. The mass doesn't change and the force of gravity doesn't change, but the surfaces are now with more or less force between them.

Example

​Sam, m = 65kg, is in an elevator that is accelerating upward with an acceleration of 2.1 m/s².

a) Draw the FB diagram.

b) Determine Sam's weight in the accelerating elevator.

​Gravitational force points down.
The normal force points up as it is holding Sam up.
The system of Sam and the elevator are accelerating upward, therefore, this is the net force.
Note that the net force is NOT part of the FB diagram.

Part B

​F_net = ma
F_net = sum of all forces

Forces in the direction of the net force are positive.
Forces in the opposite direction of the net force are negative.
In this case, up is positive and down is negative, since we are accelerating upward.

​F_net = F_N - F_g

This is our "unbalanced" equation. Were the system in equilibrium, the normal force would be equal to the gravitational force.

But, alas, we have:

F_N = F_net + F_g

And...

F_N = (65)(2.1) + (65)(9.8)

Note that we aren't using negative 9.8. This is because we are already considering direction in our equation.

F_N = 774 N

Multiple Choice

Two blocks of wood, each of mass 2 kg, are suspended from the ceiling by strings of negligible mass, as shown above.What is the tension in the upper string?

• 10 N

• 20 N

• 40 N

• 50 N

• 60 N

Multiple Choice

Two blocks of wood, each of mass 2 kg, are suspended from the ceiling by strings of negligible mass, as shown above.What is the force exerted on the upper block by the lower string?

• zero

• 10 N upward

• 10 N downward

• 20 N upward

• 20 N downward

Multiple Choice

A block of mass 2 kg is suspended from a rope, as shown above. If the tension in the rope is 10 N, the acceleration of the block is most nearly

• zero

• 2 m/s² up

• 2 m/s² down

• 5 m/s² up

• 5 m/s² down

Multiple Choice

Two blocks of masses m and M are suspended as shown above by strings of negligible mass. If a person holding the upper string lowers the blocks so that they have a constant downward acceleration, the tension in the string at point P is

• (M+m)g-ma

• (M+m)g-Ma

• Mg-(M+m)a

• Mg

• M(g-a)

Multiple Choice

A 50-kg student stands on a scale in an elevator. At the instant the elevator has a downward acceleration of 1.0 m/s² and an upward velocity of 3.0 m/s, the scale reads approximately

• 350 N

• 450 N

• 500 N

• 550 N

Multiple Choice

A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly

• 6 m/s²

• 6.7 m/s²

• 10 m/s²

• 15 m/s²

• 16.7 m/s²

Multiple Choice

A mass is suspended from the roof of an elevator by means of a spring balance. The elevator is moving upwards and the readings of the spring balance are noted as follows:

Speeding up: R_U

Constant speed: R_C

Slowing down: R_D

Which of the following is a correct relationship between the readings?

• R_U >R_C

• R_U = R_D

• R_C =R_D

• R_C< R_D

Multiple Choice

Two blocks are connected by a rope, as shown above. The masses of the blocks are 5 kg for the upper block and 10 kg for the lower block. An upward applied force of magnitude F acts on the upper block.

Question

The system is moving and accelerating upward. A pair of scissors cuts the rope. Which of the following describes the motion of the 10 kg block immediately after the rope has been cut?

• The block continues to move upward and to accelerate upward.

• The block begins to move downward but continues to accelerate upward.

• The block continues to move upward but begins to accelerate downward.

• The block begins to move downward and to accelerate downward.

Multiple Choice

Two blocks are connected by a rope, as shown above. The masses of the blocks are 5 kg for the upper block and 10 kg for the lower block. An upward applied force of magnitude F acts on the upper block.

Question

If the net acceleration is downward but has a magnitude less than g, then which has the larger magnitude, the force F or the tension in the rope?

• The tension in the rope

• Force F

• Neither. They have equal but nonzero magnitudes.

• Neither. They have equal zero magnitudes.

Multiple Choice

Two blocks are connected by a rope, as shown above. The masses of the blocks are 5 kg for the upper block and 10 kg for the lower block. An upward applied force of magnitude F acts on the upper block.

Question

If the F = 180 N, what is the tension in the rope?

• 120 N

• 100 N

• 220 N

• 200 N