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Shtirlitz [24]
3 years ago
10

The position vector of an object of mass 0.5 kg is given by r 2.0t2i+ 3.0tj m where t represents time. Which ONE of the followin

g statements is FALSE when a time of t 2.0 s has elapsed. a) The object has moved a distance of 10 m. b) The momentum of the object is 41+1.5/ kg.m.s c) The kinetic energy of the object is 18 J d) The force on the object acts perpendicular to the direction of the unit vectorj e) The magnitude of the force acting on the object is 4 N
Physics
1 answer:
Pie3 years ago
8 0

Answer:

Statement E is false.

Explanation:

Statement a says that the object would have moved a distance of 10 m.

At t = 0

x0  = 0

y0 = 0

At t= 2

x2 = 2 * 2^2 = 8

y2 = 3 * 2 = 6

d2 = \sqrt{x2^2 + y2^2}

d2 = \sqrt{8^2 + 6^2} = 10 m

Statement A is true.

Statement B says that the momentum of the object would be 4*i+1.5*j

To test this we need to know the speed.

The speed is the first derivative by time:

v = 4*t*i + 3*j

At t = 2 the speed is

v2 = 8*i + 3*j

The momentum is

P = m * v

P2 = 0.5 * (8*i + 3*j) = (4*i+1.5*j)

This statement is true.

Statement C says that the kinetic energy of the object would be 18 J.

The magnitude of the speed is

v = \sqrt{8^2 + 3^2} = 8.54 m/s

The kinetic energy is

Ek = 1/2 * m * v^2

Ek = 1/2 * 0.5 * 8.54^2 = 18 J

Statement C is true

Statement D says that the force acts perpenducular to the direction of the unit vector j.

The acceleration is the second derivative respect of time

a = 4*i + 0*j

Since there is no acceleration in the direction of j we can conclude that the force is perpendicular to the direction of j.

Statement D is true.

Statement E says that the force acting on the object is of 4 N

f = m * a

f = 0.5 * 4 = 2 N

Statement E is false.

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An object falls from the top of a building that is 25 m high. Air resistance is negligible.
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The velocity of the object s calculated as 22.1 m/s.

<h3>What is the speed of the object?</h3>

Given that we can write that;

v^2 = u^2 + 2gh

Now u = 0 m/s because the object was dropped from a height

v^2 = 2gh

v = √2 * 9.8 * 25

v = 22.1 m/s

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2 years ago
A 81 kg person sits on a 3.8 kg chair. Each leg of the chair makes contact with the floor in a circle that is 1.2 cm in diameter
tankabanditka [31]

Answer:

1.9 MPa

Explanation:

Mass of person = 81 kg

Mass of chair = 3.8 kg

Diameter of contact point = 1.2 cm = D

Radius of contact point = 1.2/2 = 0.6 cm

Total mass of chair and person = 81 + 3.8 = 84.8 kg = M

Acceleration due to gravity = 9.81 m/s²

Force acting on the floor

<em>F = Mg</em>

<em>⇒F = 84.8×9.81</em>

<em>⇒F = 831.888 N</em>

Area of the contact point

<em>A = πR²</em>

<em>⇒A = π0.006²</em>

<em>⇒A = π0.000036 m²</em>

Area of the four points is

<em>4A = 0.000144π m²</em>

Pressure

p=\frac{F}{A}\\\Rightarrow p=\frac{831.888}{0.000144\pi}\\\Rightarrow p=1838876.21\ Pa=1.83887621\times 10^6\ Pa=1.9 MPa

Pressure exerted on the floor by each leg of the chair is 1.9 MPa

5 0
3 years ago
You stand on top a building 44 m tall with a water balloon. You drop the water balloon from rest. How fast is the balloon moving
Alecsey [184]
<h2>The balloon is moving when it is halfway down the building at 20.78 m/s.</h2>

Explanation:

We have equation of motion v² = u² + 2as

Initial velocity, u = 0 m/s  

Acceleration, a = 9.81 m/s²  

Displacement, s = 0.5 x 44 = 22 m

Substituting  

v² = u² + 2as

v² = 0² + 2 x 9.81 x 22

v² = 431.64

v = 20.78 m/s

Velocity at 22 m = 20.78 m/s

The balloon is moving when it is halfway down the building at 20.78 m/s.

7 0
3 years ago
A river flows at 2m/s. The velocity of a ferry relative to the shore is 4m /s at right angle to the current. What is the velocit
monitta

The velocity of the ferry relative to the current is 4.5 m/s.

<h3>Relative velocity</h3>
  • Relative velocity is the velocity of a body as observed from the reference point of another body either stationary or in motion.

Since the river is flowing parallel to the shore and the ferry is moving perpendicular to the shore, their velocities are at right angles to each other.

The two velocities form a right angled-triangle of sides 2, 4 and a hypotenuse which gives the relative velocity of the ferry to the current.

Using Pythagoras rule:

  • c² = a² + b²
  • Let c be the hypotenuse
  • a =  velocity of the ferry, and
  • b = the velocity of the current, and

c² = 4² + 2²

c² = 16 + 4

c = 20

c = √20

c = 4.47 m/s

c ≈ 4.5 m/s

Therefore, the velocity of the ferry relative to the current is 4.5 m/s.

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