Answer:
0.033815 m/s²
12.48810875 m
Explanation:
t = Time taken = 12 s
= Final angular velocity = 95 rpm
= Initial angular velocity = 64 rpm
= Angular acceleration
= Angle of rotation
Tangential acceleration is given by
The tangential acceleration of the pedal is 0.033815 m/s²
Linear displacement would be 
Length of chain that passes in the interval is 12.48810875 m
Kinematic question!
Start with your knowns!
we want to find x!
the only kineamtic that works with this info is the third!
so we plug in our values and get
this'll equal out to -159.2 meters.
our units equal out, so we know our answer is correct!
Classically and Newtonianly, it's the sum of the chemical energy if any,
the electrical energy if any, the thermal energy if any, and the mechanical
energy consisting of potential and kinetic energy if any.
The mechanical energy, consisting of potential and kinetic energy if any, is
0.001 x [ (acceleration of gravity x height) + (1/2) (speed)² ] .
But I've got a sneaky hunch that you're not talking about any of these.
You want to know how much [ <em><u>mc</u>² </em>] there is in 1 gram of mass. No prob.
E = m c² = (0.001) x (3 x 10⁸)² = <em>9 x 10¹³ joules</em>
That's the energy that a 1,000-watt toaster uses
in <em>2,852 years</em> of continuous toasting.
Force of gravity = 'G' (mass₁)(mass₂) / (distance)²
'G' is the gravitational constant for SI units = 6.67 x10⁻¹¹ newton-meter²/kg²
You said that the force is <u>2.99 x 10⁻¹⁰</u> = (6.67x10⁻¹¹) (4) (7) / D²
Multiply each side by D² : 2.99 x 10⁻¹⁰ D² = (6.67x10⁻¹¹) (28)
Divide each side by 2.99 x 10⁻¹⁰ : D² = (28) (6.67 x10⁻¹¹) / (2.99 x 10⁻¹⁰)
Take the square root of each side: D = square root of all that
Stuff it through my calculator:
D = square root of [ (28) (6.67 x10⁻¹¹) / (2.99 x 10⁻¹⁰) ] =
√ ( 6.2462...) meters² =
<em>2.5 meters </em> (rounded)
===================
To get the feel:
-- The book weighs about 8.8 pounds (big book)
-- The lamp weighs about 15.4 pounds
-- They're about 8.2 feet apart.
-- The strength of the gravitational force
between them is about 0.000 000 001 075 of an ounce .
