Physics - Newton's Laws and Fundamental Concepts

A cinder block sitting on a frictionless surface is attached to a rope. If the rope is pulled parallel to the surface such that the block accelerates at a rate of $5\frac{m}{s^2}$ , what is the minimum amount of tension the rope must be able to support without breaking?

Explanation

This is a simple case of . In this instance, is and is $5\frac{m}{s^2}$ . Substituting, we find .

An hourglass is placed on a scale with all its sand in the upper chamber. A short time later, the sand begins to fall into the lower chamber. Which of the following best describes the reading on the scale as a function of time before any sand has accumulated in the bottom chamber?

The reading on the scale decreases slightly.

The reading on the scale stays the same.

None of these

The reading on the scale increases.

The reading on the scale is zero.

Explanation

Initially, when all the sand is in the upper chamber, the reading on the scale is constant and corresponds to the weight of the hourglass and the sand within. As some sand falls, there is no normal force on it so the scale can not register its weight. The fraction of sand that is falling is small, so there is only a small decrease in the apparent weight of the hourglass.

A object experiences a force of in its direction of motion for . What is the change in the velocity the object moved at during this time?

$21.6\frac{m}{s}$

$31.6\frac{m}{s}$

$41.6\frac{m}{s}$

$51.6\frac{m}{s}$

$61.6\frac{m}{s}$

Explanation

Let's first write down the information we are given:

We know that . This equation can simplified to $F=\frac{m*v}{t}$ since acceleration is equal to velocity over time so $a=\frac{v}{t}$ .

Let's manipulate the equation by solving for velocity so we can simply plug in the numbers we are given:

so: $v=t*\frac{F}{m}$

$4*\frac{27}{5}=21.6\frac{m}{s}$ which is our final answer.

A cinder block sitting on the ground is attached to a rope. If the rope is pulled such that the block accelerates directly upwards at a rate of $5\frac{m}{s^2}$ , what is the minimum amount of tension the rope must be able to support without breaking?

Explanation

In this case, the rope must be able to support both the force of gravity and the force required to accelerate the block. Both are given by :

$F_{gravity} = (50 kg)(9.81\frac{m}{s^2}) = 490.5 N$

$F_{accelerate} = (50 kg)(5\frac{m}{s^2}) = 250 N$

$F_{total} = 490.5 N + 250 N = 740.5 N$

A experiences a net force that increases its velocity by $17\frac{m}{s}$ from rest for . What is the magnitude of this force?

Explanation

Let's write down the information we are given:

$v=17\frac{m}{s}$

We know that . This equation can simplified to $F=m\frac{v}{t}$ since acceleration is equal to velocity over time so $a=\frac{v}{t}$ .

So we can just plug in the information we are given to solve for the Force:

$15*\frac{17}{6}=42.5N$ , which is our final answer.

A block which weighs experiences a resultant force of that increases its velocity by $83\frac{m}{s}$ . How long did this force act on the block?

Explanation

Let's first write down the information we are given:

$v=83\frac{m}{s}$

We know that . This equation can simplified to $F=\frac{mv}{t}$ since acceleration is equal to velocity over time so $a=\frac{v}{t}$ .

Let's manipulate the equation by solving for time so we can simply plug in the numbers we are given:

so: $t=m*\frac{v}{F}$

$15*\frac{83}{85}$ = which is our final answer.

A juggler throws a ball straight up into the air, which exerts air resistance on the ball. Which of the following best describes the speed of the ball after it falls and just reaches the juggler's hand?

The speed of the ball is less than when the juggler first threw it.

The speed of the ball is exactly the same as when it was released.

The speed of the ball is greater than when it was released.

The speed of the ball is zero.

None of the other answers.

Explanation

Air resistance is like a friction force that takes energy away from the ball. Because the ball has energy taken from it on the way up and the way down, there is net negative work done on the ball. The energy of the ball is not conserved and it slows down slightly compared to when it was released.

An object is pushed from rest with a force of that increases its velocity by $15\frac{m}{s}$ for . What is the mass of this object?