Two people singing off key in a choir

The period of a pendulum is measured 16 times. The average value of the period over these 16 trials is calculated to be 1.50 sec

marin [14]

Answer:

The additional trials needed is 48 trials

Explanation:

Given;

initial number of trials, n = 16 trials

the standard deviation, σ = 0.24 s

initial standard error, ε = 0.06 s

The standard error is given by;

$\epsilon = \frac{\sigma}{\sqrt{n} }$

To reduce the standard error to 0.03 s, let the additional number of trials = x

$0.03= \frac{0.24}{\sqrt{n+x} } \\\\0.03= \frac{0.24}{\sqrt{16+x} }\\\\0.03\sqrt{16+x} = 0.24\\\\\sqrt{16+x} = \frac{0.24}{0.03} \\\\\sqrt{16+x} = 8\\\\16+x = 8^2\\\\16+x = 64\\\\x = 64 -16\\\\x = 48 \ trials$

Therefore, the additional trials needed is 48 trials.

6 0

3 years ago

A goalie kicks a soccer ball straight vertically into the air. It takes 5.00 s for the ball to reach its maximum height and come

Yuliya22 [10]

Answer:

(a) vo = 24.98m/s

(b) t = 5.09 s

Explanation:

(a) In order to calculate the the initial speed of the ball, you use the following formula:

$y=y_o+v_ot-\frac{1}{2}gt^2$ (1)

y: vertical position of the ball = 2.44m

yo: initial vertical position = 0m

vo: initial speed of the ball = ?

g: gravitational acceleration = 9.8m/s²

t: time on which the ball is at 2.44m above the ground = 5.00s

You solve the equation (1) for vo and replace the values of the other parameters:

$v_o=\frac{y-y_o+1/2gt^2}{t}$

$v_o=\frac{2.44m-0.00m+1/2(9.8m/s^2)(5.00s)^2}{5.00s}\\\\v_o=24.98\frac{m}{s}$

The initial speed of the ball is 24.98m/s

(b) To find the time the ball takes to arrive to the ground you use the equation (1) for y = 0m (ground) and solve for t:

$0=24.98t-\frac{1}{2}(9.8)t^2\\\\t=5.09s$

The time that the ball takes to arrive to the ground is 5.09s

5 0

3 years ago

Type the most appropriate SI base unit (with a specific prefix as needed) for expressing each of the following.?(a) the mass of

ra1l [238]

Answer:

Explanation:

Standard International (SI) units of measurement is the acceptable global units of measure for physical quantities. they are majorly fundamental units.

Thus,

(a) The mass of a sport car is measured in kilograms (kg).

(b) The distance from your home to your school is measured in meters (m).

(c) The mass of an elephant is measured in kilograms (kg).

(d) The diameter of a large pizza is measure in meters (m).

(e) A semester at your school is measured in weeks.

(f) The time for light to travel from the sun to the earth is expressed in seconds (s).

(g) The time it takes to fly from New York to California is in seconds (s).

(h) Your mass is measured in kilograms (kg).

(i) The length of the Prime Meridian is expressed in meters (m).

(j) Your height is expressed in meters (m).

7 0

3 years ago

What is the total kinetic energy of a hoop of radius 1 m and mass 2 kg that rolls at an

nevsk [136]

Answer:

12

Explanation:

What is the total kinetic energy of a hoop of radius 1 m and mass 2 kg that rolls at an

angular velocity of 1 rad/s?

3 0

3 years ago

A truck with 28-in.-diameter wheels is traveling at 50 mi/h. Find the angular speed of the wheels in rad/min, *hint convert mile

solong [7]

Answer:

Angular speed ω=3771.4 rad/min

Revolution=5921 rpm

Explanation:

Given data

$d=28in\\r=d/2=28/2=14in\\v=50mi/hr$

To find

Angular speed ω

Revolution per minute N

Solution

First we need to convert the speed of truck to inches per mile

as

1 mile=63360 inches

1 hour=60 minutes

so

$v=(50*\frac{63360}{60} )\\v=52800in/min$

Now to solve for angular speed ω by substituting the speed v and radius r in below equation

$w=\frac{v}{r}\\ w=\frac{52800in/min}{14in}\\ w=3771.4rad/min$

To solve for N(revolutions per minute) by substituting the angular speed ω in the following equation

$N=\frac{w}{2\pi }\\ N=\frac{3771.4rad/min}{2\pi }\\ N=5921RPM$

3 0

3 years ago