A machine has an efficiency of 20%. Find the input work if the output work is 140J.

A block is balanced on top of a frictionless sphere of radius R. When the block is given a slight nudge it starts to slide down

Nataly_w [17]

Answer: $\frac{R}{3}$

Explanation:

Given

Sphere of Radius R

Suppose mass of block is m

At any instant \theta Normal reaction(N) and weight(mg) is acting such that

$mg\sin \theta -N=\frac{mv^2}{R}$ , where v is velocity of block at any angle \theta

When block is just about to leave then N=0

therefore

$mg\sin \theta =\frac{mv^2}{R}$

$v^2=gR\sin \theta$ -------------------1

Also by conserving Energy we get

Potential Energy=kinetic Energy of block

$mgh=\frac{mv^2}{2}$

here h=vertical distance traveled by block

From diagram

$h=R-R\sin \theta$

$h=R(1-\sin \theta )$

$mgR(1-\sin \theta )=\frac{mv^2}{2}$

$2gR(1-\sin \theta )=v^2$ -----------------2

From 1 and 2

$2(1-\sin \theta )=\sin \theta$

$3\sin \theta =2$

$\sin \theta =\frac{2}{3}$

Thus from this value of h is

$h=R(1-\sin \theta )$

$h=R(1-\frac{2}{3})$

$h=\frac{R}{3}$

3 0

4 years ago

While goofing off at the ice skating rink, a student takes off her shoes and places each of them on the ice. Her friend, a hocke

sukhopar [10]

Answer:

Right shoe

Explanation:

Let the mass and velocity of incoming puck be m and v respectively.

Momentum of the colliding puck will be mv

In case of first case , the momentum of puck becomes zero so change in momentum after collision with left shoe

= mv - 0 = mv

If time duration of collision be t

rate of change of momentum

= mv / t

This is the force exerted by puck on the left shoe .

Now let us consider collision with right shoe

momentum after collision with right shoe

- mv

change in momentum

= mv - ( - mv ) = 2mv

If time duration of collision be t

rate of change of momentum

= 2mv / t

This is the force exerted by puck on the right shoe .

Since the force on the right shoe is more , this shoe will have greater speed

after collision.

6 0

3 years ago

When white light is incident on a prism, which one of the resulting color components will have the lowest index of refraction?

soldi70 [24.7K]

Blue has the lowest index of refraction

3 0

3 years ago

Read 2 more answers

What is the most abundant element in the universe?<br> A. helium<br> B. hydrogen<br> C. carbon

Naya [18.7K]

The answer is Carbon

3 0

3 years ago

Read 2 more answers

Marco wants to investigate the chemical properties of sodium bicarbonate, or baking soda. He plans to carry out the tests below.

SSSSS [86.1K]

Answer:

The options are:

Test 1: Mix a teaspoon of sodium bicarbonate into a cup of warm water to see if it dissolves.

Test 2: Mix a teaspoon of sodium bicarbonate into a cup of vinegar to see if it fizzes.

Test 3: Heat a teaspoon of sodium bicarbonate in the oven to see if its melting point is less than 400 degrees Fahrenheit.

Which statement provides the best assessment of his tests?

The answer is Test 2: Mix a teaspoon of sodium bicarbonate into a cup of vinegar to see if it fizzes.

This is because it will indicate the chemical property of the sodium bicarbonate as a result of its reaction with another chemical compound, a vinegar.

Tests 1 and 3 will show a physical property of the substance as a result of the physical characteristics such as solubility and melting point .

6 0

3 years ago