1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Agata [3.3K]
3 years ago
13

In a second experiment, you decide to connect a string which has length L from a pivot to the side of block A (which has width d

) so that the block will be constrained to go in a circular path about the pivot once it leaves the launcher. What relationship would allow you to write an expression for the maximum tension in the string during the motion? Justify your choice and explain how the maximum tension would depend on the variables given in the problem.
Physics
1 answer:
Salsk061 [2.6K]3 years ago
8 0

Answer:

The answer is in the explanation

Explanation:

A)

i) The blocks will come to rest when all their initial kinetic energy is dissipated by the friction force acting on them. Since block A has higher initial kinetic energy, on account of having larger mass, therefore one can argue that block A will go farther befoe coming to rest.

ii) The force on friction acting on the blocks is proportional to their mass, since mass of block B is less than block A, the force of friction acting on block B is also less. Hence, one might argue that block B will go farther along the table before coming to rest.

B) The equation of motion for block A is

m_{A}\frac{\mathrm{d} v}{\mathrm{d} t} = -m_{A}g\nu_{s}\Rightarrow \frac{\mathrm{d} v}{\mathrm{d} t} = -\nu_{s}g \quad (1)

Here, \nu_{s} is the coefficient of friction between the block and the surface of the table. Equation (1) can be easily integrated to get

v(t) = C-\nu_{s}gt \quad (2)

Here, C is the constant of integration, which can be determined by using the initial condition

v(t=0) = v_{0}\Rightarrow C = v_{0} \quad (3)

Hence

v(t) = v_{0} - \nu_{s}gt \quad (4)

Block A will stop when its velocity will become zero,i.e

0 = v_{0}-\nu_{s}gT\Rightarrow T = \frac{v_{0}}{\nu_{s}g} \quad (5)

Going back to equation (4), we can write it as

\frac{\mathrm{d} x}{\mathrm{d} t} = v_{0}-\nu_{s}gt\Rightarrow x(t) = v_{0}t-\nu_{s}g\frac{t^{2}}{2}+D \quad (6)

Here, x(t) is the distance travelled by the block and D is again a constant of integration which can be determined by imposing the initial condition

x(t=0) = 0\Rightarrow D = 0 \quad (7)

The distance travelled by block A before stopping is

x(t=T) = v_{0}T-\nu_{s}g\frac{T^{2}}{2} = v_{0}\frac{v_{0}}{\nu_{s}g}-\nu_{s}g\frac{v_{0}^{2}}{2\nu_{s}^{2}g^{2}} = \frac{v_{0}^{2}}{2\nu_{s}g} \quad (8)

C) We can see that the expression for the distance travelled for block A is independent of its mass, therefore if we do the calculation for block B we will get the same result. Hence the reasoning for Student A and Student B are both correct, the effect of having larger initial energy due to larger mass is cancelled out by the effect of larger frictional force due to larger mass.

D)

i) The block A is moving in a circle of radius L+\frac{d}{2} , centered at the pivot, this is the distance of pivot from the center of mass of the block (assuming the block has uniform mass density). Because of circular motion there must be a centripetal force acting on the block in the radial direction, that must be provided by the tension in the string. Hence

T = \frac{m_{A}v^{2}}{L+\frac{d}{2}} \quad (9)

The speed of the block decreases with time due to friction, hence the speed of the block is maximum at the beginning of the motion, therfore the maximum tension is

T_{max} = \frac{m_{A}v_{0}^{2}}{L+\frac{d}{2}} \quad (10)

ii) The forces acting on the block are

a) Tension: Acting in the radially inwards direction, hence it is always perpendicular to the velocity of the block, therefore it does not change the speed of the block.

b) Friction: Acting tangentially, in the direction opposite to the velocity of the block at any given time, therefore it decreases the speed of the block.

The speed decreases linearly with time in the same manner as derived in part (C), using the expression for tension in part (D)(i) we can see that the tension in the string also decreases with time (in a quadratic manner to be specific).

You might be interested in
What is a direct result of having greenhouse gases in the atmosphere?
Shalnov [3]

Answer:

Well this is tough. I'm not sure but you are smart and can push through it. YOU DONT need the someone telling you the answer when it is inside you.

hope this helps p

3 0
2 years ago
Read 2 more answers
A net force of 3000 N is accelerating a 1200 kg elevator upward. If the elevator starts from rest, how long will it take to trav
alexdok [17]

F = net force acting on the elevator in upward direction = 3000 N

m = mass of the elevator = 1200 kg

a = acceleration of the elevator = ?

Acceleration of the elevator is given as

a = F/m

a = 3000/1200

a = 2.5 m/s²

v₀ = initial velocity of the elevator = 0 m/s

Y = displacement of the elevator = 15 m

t = time taken

Using the kinematics equation

Y = v₀ t + (0.5) a t²

15 = (0) t + (0.5) (2.5) t²

t = 3.5 sec

5 0
3 years ago
A marble rolling at a speed of 2.71 m/s falls of the end of a table that is 1.25 m high. How far from the base of the table does
katrin [286]

Answer:

The marble lands at a distance of 1.36 m from the base of the table.

Explanation:

The motion of the marble falling off the table is a projectile with initial velocity in the horizontal direction only.

The motion can be solved in two directions, the horizontal and vertical direction.

Along the vertical direction, the initial velocity is 0 m/s as it has only horizontal component initially. Also acceleration in the vertical direction is acceleration due to gravity.

Let us use equation of motion in vertical direction.

y-y_0=v_{0y}t+\frac{1}{2}at^2

Where,

v_{0y}\rightarrow \textrm{vertical component of the initial velocity}.\\y\rightarrow \textrm{final position of the marble}\\y_0\rightarrow \textrm{initial vertical position}\\a_y\rightarrow \textrm{acceleration in the vertical direction}\\t\rightarrow \textrm{time taken to reach bottom}

Now, plug in 0 for y, 1.25 for y_0, 0 for v_{0y}, -9.8 for a_y. This gives,

0-1.25=0+\frac{1}{2}(-9.8)t^2\\-1.25=-4.9t^2\\t^2=\frac{-1.25}{-4.9}\\t^2=0.255\\t=\sqrt{0.255}=0.501\ s

Therefore, time to reach bottom is 0.501 s.

Now, consider the horizontal motion. There is no acceleration in the horizontal direction. So, distance is given as the product of horizontal velocity and time taken.

Horizontal distance covered by the marble is given as:

x=v_{0x}\times t=2.71\times 0.501=1.36 \textrm{ m}

Therefore, the marble lands at a distance of 1.36 m from the base of the table.

6 0
3 years ago
How does energy from the sun affect the motion of molecules in a gas compared to molecules in a liquid?
AnnZ [28]
Molecules in a gas move faster than in a liquid.

hope it helps.
3 0
3 years ago
Read 2 more answers
These three forces act on art object:
denpristay [2]

Answer:

12N S

Explanation:

their are many student who can not get answer on time and step by step answer.so there are

a wats up group of experienced experts who helps you for free with step by step answer.just join this and get answer.

just scan it

5 0
3 years ago
Other questions:
  • How can the speed of solvent molecules be slowed down?
    10·1 answer
  • Which of these best describes how an appropriate star chart is selected to locate objects in the sky
    10·1 answer
  • How much heat is required to convert 500g of liquid water at 28°C into steam at 150 °C? Take the specific heat capacity of water
    6·1 answer
  • When viewed in yellow light, an object that reflects all the colors of light will appear_____.
    15·1 answer
  • A 31 kg crate full of very cute kittens is placed on an incline that is 17° below the horizontal. The crate is connected to a sp
    14·1 answer
  • A container of water is lifted vertically 3.0m
    15·1 answer
  • It was a children versus grown-ups competition at school. One event required the adult to throw a basketball as far as he could.
    6·2 answers
  • A hypothetical atom has three energy levels: the ground-state level and levels 1.50 eV and 5.00 eV above the ground state. What
    5·1 answer
  • An apple is whirled round in a horizontal circle on the end of a string which is tied to the stalk. It is whirled faster and fas
    5·1 answer
  • which of the following statements is a reasonable conclusion about the Arctic ecosystem? a)The number of offspring produced is a
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!