A golf ball is hit with an initial velocity of 20m/s at an angle of 30° to the horizontal. calculate;

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneou

Roman55 [17]

Answer:

The solid sphere will reach the bottom first.

Explanation:

In order to develop this problem and give it a correct solution, it is necessary to collect the concepts related to energy conservation. To apply this concept, we first highlight the importance of conserving energy so we will match the final and initial energies. Once this value has been obtained, we will concentrate on finding the speed, and solving what is related to the Inertia.

In this way we know that,

$\Delta KE = - \Delta PE$

$KE_t + KE_r = mgh$

We know as well that the lineal and angular energy are given by,

$KE_r = \frac{1}{2}I\omega^2$

And the tangential kinetic energy as

$KE_t = \frac{1}{2} mv^2$

Where $\omega = \frac{v}{R}$

Replacing

$\frac{1}{2}mv^2 + \frac{1}{2}I\frac{v}{R} = mgh$

Re-arrange for v,

$v=\sqrt{\frac{2mgh}{m+I/R^2}}$

We have here three different objects: solid cylinder, hollow pipe and solid sphere. We need the moment inertia of this objects and replace in the previous equation found, then,

For hollow pipe:

$I_{hp}=mR^2$

$v_{hp}=\sqrt{\frac{2mgh}{m+(mR^2)/R^2}}$

$v_{hp}=\sqrt{\frac{2mgh}{m+m)}$

$v_{hp}=\sqrt{gh}$

For solid cylinder:

$I_{sc}=\frac{1}{2}mR^2$

$v_{sc}=\sqrt{\frac{2mgh}{m+(1/2mR^2)/R^2}}$

$v_{sc}=\sqrt{\frac{2mgh}{m+1/2m}}$

$v_{sc}=\sqrt{\frac{3}{4}gh}$

For solid sphere,

$I_{ss}=\frac{2}{5}mR^2$

$v_{ss}=\sqrt{\frac{2mgh}{m+(2/5mR^2)/R^2}}$

$v_{ss}=\sqrt{\frac{2mgh}{m+2/5m}}$

$v_{ss}=\sqrt{\frac{10}{7}gh}$

Then comparing the speed of the three objects we have:

$v_{hp}$

$\sqrt{gh}$

3 0

4 years ago

What force works against friction? <br> Inertia<br> Potential <br> Kinetic

Oksanka [162]

Kinetic, as inertia means to remain unchanged.

6 0

4 years ago

Read 2 more answers

When the magnetic flux through a coil of wire changes, what is generated between the ends of the coil

Gnesinka [82]

When a magnet is moved into a coil of wire, changing the magnetic field and magnetic flux through the coil, a voltage will be generated in the coil according to Faraday's Law.

4 0

3 years ago

What will occur when the trough of wave A overlaps the trough of wave B?

densk [106]

Constructive interference will occur, which means the waves will combine.

In destructive inference, the waves cancel each other out.

Hope this helps :)

3 0

3 years ago

Read 2 more answers

A projectile is fired straight upward with an initial veloc- ity of 100 m=s from the top of a building 20 m high and falls to th

SVETLANKA909090 [29]

Answer:

The answer to your question is:

a) h max = 529.7 m

b) t = 20.4 s

c) t = 20.6 s

Explanation:

a) h max = -(vo)² / 2g

= 100² / 2(9.81)

= 10000 / 19.62

= 509.7 m

total height = 509.7 + 20 = 529.7 m

b)

h = gt² / 2

t = √ 2h / g

t = √ 2(509.7)/9.81

t = √ 103.91

t = 10.19 s

total time = 2 x t = 2 x 10.19 = 20.4 s

c)

h = vot + 1/2gt²

20 = 100t + 1/2(9.91) t²

4.9t² + 100 t -20 = 0 quadratic equation

t = 0.19 s

Total time = 0.19 + 20.4 = 20.6 s

5 0

3 years ago