AP Physics C: Electricity and Magnetism - Interpreting Linear Motion Diagrams

A guillotine blade weighing is accelerated upward into position at a rate of $2.0\frac{m}{s^2}$ .

What is the tension on the rope pulling the blade, while it is accelerating into position?

Explanation

The tension in the rope is the sum of the forces acting on it. If one considers that the net force on an object must equal the mass of the object times the acceleration of the object, the net force on the object must be the force due to tension from the rope minus the force due to gravity.

$F_{T}-F_{g}=ma$

Rearrange the equation.

$F_{T}=ma+F_{g}$

Plug in known values.

$F_T=41kg\cdot2\frac {m}{s^2} + 400N$

Atwood's machine consists of two blocks connected by a string connected over a
pulley as shown. What is the acceleration of the blocks if their masses are and .

Assume the pulley has negligible mass and friction.

Explanation

From the force diagram above, we can see that tension is pulling up on both sides of the string and gravity is pulling down on both blocks. With this information we can write 2 force equations:

If we add the two equations together, we get:

where

Solving for , we get

Two objects moving in one dimension created the following velocity vs. time graph:

Velocity time graph labeled

From the graph above, which object has traveled a greater distance from its starting position when $\small t=5s$ ?

Object 1

Object 2

They have travelled an equal distance

It cannot be determined from the graph

None of these

Explanation

Since this is a graph of velocity vs. time, its integral is distance travelled. We can estimate the integral by looking at the area under the curves. Since Bbject 1 has a greater area under its velocity curve, it has covered a greater distance. Its velocity is greater that Object 2's for the entire time, so it makes sense that it will travel farther.

A guillotine blade weighing is accelerated upward into position at a rate of $2.0\frac{m}{s^2}$ .

What is the the approximate mass of the guillotine blade?

Explanation

The force of gravity on the blade is , which is the same as $400\frac{kg\cdot m}{s^2}$

This unit relationship comes from Newton's second law.

is the mathematical expression of Newton's second law. The units for force must be a product of the units for mass and the units for acceleration.

Solve the expression by plugging in known values.

$400 \frac{kg\cdot m}{s^2}=m \cdot 9.8\frac{m}{s^2}$

$\frac{400}{9.8}kg=mass\approx41kg$

An object is moving in two dimensions. Its vertical motion relative to the horizontal motion is described by the equation $\small y=ax^2+bx +c$ . Its motion in the horizontal direction is described by the equation $\small x=v_{x}t$ . What is the object's velocity is the direction in terms of its horizontal position $\small x$ ?

$\small v_{y}=(2ax+b)v_{x}$

$\small 2ax+b$

$\small (2av_{x}t+b)v_{x}$

$\small a$

$\small b$

Explanation

The y velocity is thetime derivative of the $\small y$ position, and not the $\small x$ derivative. In order to find it, use the chain rule:

$\frac{dy}{dt}=\left(\frac{dy}{dx}\right) \frac{dx}{dt}$

$\frac{dy}{dx}= 2ax + b$

Of course, $\frac{dx}{dt} =v_{x}$

Two objects moving in one dimension created the following velocity vs. time graph:

Velocity time graph labeled

From the graph above, what is true about the two objects at time $\small t=5s$ ?

They are moving at the same speed

They are at the same position

They have travelled the same distance from their starting positions

They are both at rest (not moving)

One object is passing the other

Explanation

Since this is a graph of velocity and not position, the curves intersect where the velocities match. Since we do not know the starting position, we do not know where the objects are relative to one another.

Interpreting Linear Motion Diagrams

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