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kow [346]
3 years ago
5

You and your best friend are bored on a saturday afternoon and decide to measure the impulse acting on a basketball when it boun

ces off the ground. the ball with a mass of m is dropped from rest at a height h. assume no fritcional forces are in play such that the ball bounces as a perfectly elastic colision.
derive an experession for the velocity of the ball jus before it collides with the ground.
Physics
2 answers:
grigory [225]3 years ago
7 0

Answer:

v = √(2gh)

Assuming g = 9.81m/s^2

v = √(19.62h)

Explanation:

Let v represent the speed of the ball just before it collide with the ground.

Applying the equation of motion;

v^2 = u^2 + 2as

Where;

v = final velocity

u = initial speed = 0 (starting from rest)

a = acceleration= g acceleration due to gravity

s = distance covered = h

So, substituting the values;

v^2 = 0^2 + 2gh

v^2 = 2gh

v = √(2gh)

Assuming g = 9.81m/s^2

v = √(19.62h)

Burka [1]3 years ago
4 0

Answer:

V = (19.62h)^0.5

Explanation:

We can apply the principle of conservation of momentum in this case.

The potential energy due to the height of fall is transformed into the kinetic energy of the ball as it falls.

PE = mgh

Where m is the mass of the ball,

g is the acceleration due to gravity = 9.81 m/s2,

h is the height of fall.

The kinetic energy of the ball = 1/2(mv^2)

Where c is the velocity of the ball.

Equating both energy,

mgh = 1/2(mv^2)

2gh = v^2

v = (2gh)^0.5 = (19.62h)^0.5

Or velocity V is equal to the square root of (19.62h)

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8 0
3 years ago
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A rope of negligible mass passes over a uniform cylindrical pulley of 1.50kg massand 0.090m radius. The bearings of the pulley h
boyakko [2]

Answer:

Explanation:

mass of pulley, m3 = 1.5 kg

Radius of pulley, R = 0.09 m

mass of monkey, m2 = 4.5 kg

mass of banana bunch, m1 = 3 kg

Let a is teh acceleration ans T1 and T2 be the tension in the rope.

The moment of inertia of the pulley

I = 0.5 x m3 x R² = 0.5 x 1.5 x 0.09 x 0.09 = 0.006075 kgm²

According to Newton's second law

T1 - m1 g = m1 x a .... (1)

m2 g - T2 = m2 x a ..... (2)

(T2 - T1 ) x R = I x α    

where, α is the angular acceleration

α = a / R

(T2 - T1)R = 0.5 x m3 x R² x a / R

T2 - T1 = 0.5 x m3 x a ..... (3)  

from (1), (2) and (3)

a = \frac{m_{2}-m_{1}}{m_{1}+m_{2}+\frac{m_{3}}{2}}\times g

a = \frac{4.5-3}{3+4.5+0.75}\times 9.8

a = 1.78 m/s²

from equation (1)

T1 = m1 ( g + a) = 3 ( 9.8 + 1.78) = 34.77 N

from equation (2)

T2 = m2 (g - a) = 4.5 (9.8 - 1.78) = 36.13 N

4 0
3 years ago
A quarterback passes a football from height h = 2.1 m above the field, with initial velocity v0 = 13.5 m/s at an angle θ = 32° a
SOVA2 [1]

Answer:

a)    x = v₀² sin 2θ / g

b)    t_total = 2 v₀ sin θ / g

c)    x = 16.7 m

Explanation:

This is a projectile launching exercise, let's use trigonometry to find the components of the initial velocity

        sin θ = v_{oy} / vo

        cos θ = v₀ₓ / vo

         v_{oy} = v_{o} sin θ

         v₀ₓ = v₀ cos θ

         v_{oy} = 13.5 sin 32 = 7.15 m / s

         v₀ₓ = 13.5 cos 32 = 11.45 m / s

a) In the x axis there is no acceleration so the velocity is constant

         v₀ₓ = x / t

          x = v₀ₓ t

the time the ball is in the air is twice the time to reach the maximum height, where the vertical speed is zero

          v_{y} = v_{oy} - gt

          0 = v₀ sin θ - gt

          t = v_{o} sin θ / g

         

we substitute

       x = v₀ cos θ (2 v_{o} sin θ / g)

       x = v₀² /g      2 cos θ sin θ

       x = v₀² sin 2θ / g

at the point where the receiver receives the ball is at the same height, so this coincides with the range of the projectile launch,

b) The acceleration to which the ball is subjected is equal in the rise and fall, therefore it takes the same time for both parties, let's find the rise time

at the highest point the vertical speed is zero

          v_{y} = v_{oy} - gt

          v_{y} = 0

           t = v_{oy} / g

           t = v₀ sin θ / g

as the time to get on and off is the same the total time or flight time is

           t_total = 2 t

           t_total = 2 v₀ sin θ / g

c) we calculate

          x = 13.5 2 sin (2 32) / 9.8

          x = 16.7 m

5 0
3 years ago
A particular inductor is connected to a circuit where it experiences a change in current of 0.8 amps every 0.10 sec. If the indu
nadya68 [22]

Answer:

0.4

Explanation:

Given that a particular inductor is connected to a circuit where it experiences a change in current of 0.8 amps every 0.10 sec. If the inductor has a self-inductance of 2.0 V, what is the inductance

Using the power formula

P = IV

Substitute all the parameters

P = 0.8 × 2

P = 1.6 W

But P = I^2 R

Substitute power and current

1.6 = 0.8^2 R

R = 1.6 / 0.64

R = 2.5 ohms

Inductance = reciprocal of resistance

Inductance = 1 / 2.5

Inductance = 0.4

4 0
3 years ago
1. Which of the following statements best describes matter?
Rashid [163]

Answer:

Matter is anything that has mass

Explanation:

The word "matter" refers to anything that has mass, either organic or inorganic. Matter is made up of atoms, which consists of a nucleus (made up of protons, positively charged, and neutrons, electrically neutron) and electrons which revolve around the nucleus.

The number of protons in the atom determine the element: there are more than 100 different elements in nature, with different properties depending on the number of electrons they have.

Matter can be in three different states also:

- solid: the atoms are tightly bond to each other, so they cannot move

- liquids: atoms are not bond to each other, so they can slide past each other, but still they have some intermolecular forces that keep them close to each other

- gas: atoms are free to move, as there are no forces that keep them close to each other

7 0
3 years ago
Read 2 more answers
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