A 14.0 kg cart is coasting down a street at a steady speed of 7.00 m/s. what is the kinetic energy of the cart?

The system consists of a 20-lb disk A, 4-lb slender rod BC, and a 1-lb smooth collar C. If the disk rolls without slipping, dete

dlinn [17]

Answer:

The velocity of the collar will be 3.076 ft/s

Explanation:

Given data

weight of the disk, Wa = 20lb

weight of rod BC, Wbc = 4lb

weight of collar, Wc = 1lb

Considering the equation of equilibrium

Vb = 1.5Wbc

Wa = 1.875 Wbc

to calculate the velocity of the collar using energy conservation equation

T1 + V1 = T2 + V2

$0+4(1.5 \sin 45)+2(3 \sin 45)=\frac{1}{2}\left(\frac{1}{2}\left(\frac{20}{32.2}\right)(0.8)\right)$

=> $(1.875 W b c)+\frac{1}{2}\left(\frac{20}{32.2}\right)(1.5 W b c)+\frac{1}{2}\left(\frac{20}{32.2}\right)$

=> $(1.5 W b c) \frac{1}{2}\left\{\frac{1}{12}\left(\frac{4}{32.2}\right)(3)\right\}+\frac{1}{2}\left(\frac{1}{32.2}\right)$

=> $(2.598 W b c)+4(1.5 \sin 0)+2(3 \sin 0)$

Wbc = 1.18rad/sec

i.e.

$V _c=2.598 \times 1.18$

= 3.076 ft/ s

5 0

3 years ago

An astronaut lands on another planet and wishes to determine the acceleration due to gravity.the astronaut measure a period of 0

jarptica [38.1K]

Answer:

1.927 m/s^2

Explanation:

period = 2 pi sqrt ( l/g)

3.2 = 2 pi sqrt (.5/g) =1.927 m/s^2

5 0

3 years ago

The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 54/(7 + x2 + y2), where T is measured in °C and x,

ANTONII [103]

Answer:

dt/dx = -0.373702

dt/dy = -1.121107

Explanation:

Given data

T(x, y) = 54/(7 + x² + y²)

to find out

rate of change of temperature with respect to distance

solution

we know function

T(x, y) = 54 /( 7 + x² + y²)

so derivative it x and y direction i.e

dt/dx = -54× 2x / (7 +x² + y²)² .........................1

dt/dy = -54× 2y / (7 + x² + y²)² .........................2

now put the value point (1,3) as x = 1 and y = 3 in equation 1 and 2

dt/dx = -54× 2(1) / (7 +(1)² + (3)²)²

dt/dx = -0.373702

and

dt/dy = -54× 2(3) / (7 + (1)² + (3)²)²

dt/dy = -1.121107

7 0

3 years ago

Figure one, voltmeters

slava [35]

Answer:

(i) Half

(ii) 3 V

(iii) V₁

Explanation:

(i) The given parameters are;

The circuits have identical resistances

The number of resistors in circuit 1 = 1 resistor

The number of resistors in circuit 2 = 2 resistors

Let 'R' represent the value of each resistor, we have;

The total resistance of circuit 1 = R Ohm

The total resistance of circuit 3 = 2·R Ohm

∴ The total resistance of circuit 1 = (1/2) × The total resistance of circuit 3

∴ The resistance of circuit 1 is <u>half</u> the resistance of circuit 3

(ii) The potential difference of each cell, V = 1.5 volts

The number of cells in circuit 2 = 2 cells

The total potential difference of the cells of circuit 2 = 2 × 1.5 volts = 3 × volts = 3 V.

The voltmeter reading = The potential difference across the cell or cells it is applied

∴ The voltmeter reading on voltmeter, V₂, applied across the cells of circuit 2 = 3 V

(iii) The voltmeter reading V₁ = 1.5 V

The voltmeter reading V₂ = 3 V

The voltmeter reading V₃ = 4.5/(2·R) × R = 2.25 V

Therefore, the voltmeter reading with the smallest volt, is V₁ = 1.5 V

6 0

3 years ago

a person can throw a 300 gram ball at 25 m/s the maximum height the person can throw the ball on Earth?

jolli1 [7]

Answer:

Elevation =31.85[m]

Explanation:

We can solve this problem by using the principle of energy conservation. This consists of transforming kinetic energy into potential energy or vice versa. For this specific case is the transformation of kinetic energy to potential energy.

We need to first identify all the input data, and establish a condition or a point where the potential energy is zero.

The point where the ball is thrown shall be taken as a reference point of potential energy.

$E_{p} = E_{k} \\where:\\E_{p}= potential energy [J]\\ E_{k}= kinetic energy [J]$

m = mass of the ball = 300 [gr] = 0.3 [kg]

v = initial velocity = 25 [m/s]

$E_{k}=\frac{1}{2} * m* v^{2} \\E_{k}= \frac{1}{2} * 0.3* (25)^{2} \\E_{k}= 93.75 [J]$

$93.75=m*g*h\\where:\\g = gravity = 9.81 [m/s^2]\\h = elevation [m]\\replacing\\h=\frac{E_{k}}{m*g} \\h=\frac{93.75}{.3*9.81} \\h=31.85[m]$

5 0

4 years ago