FE Physics

Formulas & Explanation

Formulas & Explanation

Dutch version

**
Motion in Two Dimensions**

**
**

**
Projectile Motion**

*
Example 1*

From a tower (height : 50 m)
an object is projected horizontally
with a velocity of 20 ms^{-1}

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Ignoring the
air resistance:

a.
Determine at what place the object hits the ground, ignoring the air
resistance ?

b.
With what velocity does that happen ?

c.
With what angle the object hits the ground ?

Solution:

The directions to the right
and upward have been chosen as positive.

a.
In the vertical (y)
direction the movement has a constant
acceleration due the gravity.

a_{y
}= g = - 9.81 m
s^{-2}.
Initial velocity in y direction = 0 ms^{-1}

Δ Y = ½ g t^{2
} - 50 = ½ -9.81 t^{2 }
t^{2} =
10.20 t =
3.2 s

In the
horizontal (x)direction the object has a constant velocity

ΔX
= v_{x}
t
x = 20 x 3.2 = 64 m

The object
hits the ground at 64 m from the base of the tower.

b.
The velocity in x - direction
remains constant.

v_{x}
van 20 m/s

v_{y}
= g t = -9.81 x 3.2 = -31.39 m/s (
minus because the direction of the velocity is downward)

The magnitude of the final velocity is to be determined using the Pythagorean
theorem

v^{2}
= v_{x}^{2
}+ v_{y}^{2}
v^{2} = 20^{2} +
31.39^{2} v^{2} =
1385.33 v = 37.2 m/s

**
**

c.
tan
α = v_{y}/v_{x
}
=
31.39/20 = 1.5695
α
= 57.5^{
o}

**
**

**Uniform Circular
Motion
**

A disc
rotates in a horizontal plane
with 360 revolutions
per minute

At a distance of 20 cm from
the center is a block with a mass of 100 g.

frequency f =
360 rev/minute =6 rev /second
f = 6 Hz

period
T=1/f = 1/6 = 0.17 s

speed
of the block
v = (2
π r) / T = (2 π
0.20)/0.17 = 7.39 m/s

angular velocity
ω = (2
π) / r = (2 π)
/0.20 = 31.4 rad/s

centripetal acceleration
of the block
a_{c} = v^{2}/r = 7.39^{2}/0.20 = 2.73 x 10^{2}
ms^{-2}

*
*

*
Remark*

In an uniform circular motion is the
speed constant

The acceleration is directed
toward the center of the circular path. This causes a change in direction of the
velocity. The speed (magnitude of the velocity) does not change.

(Centripetal Force : see
chapter Force and Torque)