What is the velocity in miles per hour?

Question

The "Niagara Falls" water slide to waterpark and has a height of 76.0 feet (23.2 meters). Because the slide is not completely vertical the total length of the slide is 90.0 feet (27.4 meters). A 70.0 kg person slides down this slide starting from rest.

a) If the slide is frictionless, what should the person's velocity be at the bottom of the slide in meters/second?

b) What is the velocity in miles per hour?

c)What if there was friction between the slide and the person. If the velocity of the person at the bottom of the slide was really 38.2 mi/hour how much energy was converted to Thermal Energy in this problem?

d) From what you founded above, What must the magnitude of the friction force have been? (assuming friction force remained constant and acts the same throughout the slide's total length)

please focus on c and d part because i am getting wrong answer from everyone

Answer 1

Given Mass = 70 Kg ,h = 23.2 m, Distance effective = 27.4 m

mgh = 1/2 (mv² )

V = sqrt (2gh) = sqrt 2*9.8*23.2 = 21.32 m/s = 47.7 miles /hr

V ( actual ) = 38.2 miles /hr = 17.07 m/s

Loss in K E = 1/2M( 21.32*21.32 - 17.07*17.07 ) = 0.5 * 70*163.15 = 5710.6 J

So work done by force of friction =5710.6 J = Force * Effective distance

Force = Work done against friction/ Effective distance

So force = 5710.6/ 27.4 = 208.4 N

Answer 2

Hello there!

a. This seems like a Conservation of Energy problem. Remember that " energy cannot be created or destroyed; it changes forms. " Having stated this, we must know ( 1 ) what the initial potential energy ( PE ) of the person is, and ( 2 ) we must realize that the potential energy has been converted into kinetic energy ( KE ), which is the energy of motion.

Let's set this equivalency into equation form: Energy is quantified in units of Joules ( J ). Potential energy ( PE ) = ( m )( g )( h ), where m = mass, g = gravitational constant of acceleration, and h = height above the ground. The kinetic energy equation is KE = ( 1 / 2 )( m )( v^2 ), where m = mass, and v = velocity ( squared ). After setting the ( PE ) and ( KE ) expressions equal to one another, we solve the equivalency for ( v ): ( m )( g )( h ) = ( 1 / 2 )( m )( v^2 ). Dividing ( m ) out of the equation gives us ( g )( h ) = ( 1 / 2 )( v^2 ). Now, we multiply each side by ( 2 ) to get ( 2 )( g )( h ) = ( v^2 ). Therefore, the final velocity should be ( v ) = ( square root of 2gh ). Substituting our variables with numeric values gives us ( sqrt ( 2 )( 9.8m / s^2 )( 23.3m ) = 21.3m / s.

Let's now convert ( 21.3 m / s ) to ( miles / hour ). We must convert meters ( m ) to miles, and we must convert seconds ( s ) to hours. We must also be sure to use the appropriate conversion fractions in the multiplication. ( 1 meter = 0.000621371 miles ), and ( 3,600 seconds = 1 hour ). Therefore, ( 21.3 m / s )( 0.000621371 mi / 1m )( 3,600 s / 1h ) = 47.80 mi / h.

In part c. we must determine how much energy was lost. We are given the final velocity, but we must convert it to metric units. Subsequently, we can plug ( v ) into the kinetic energy equation of ( 1 / 2 )( m )( v^2 ). The value we obtain will be subtracted from the theoretical value of kinetic energy obtained from sliding down a frictionless slide ( final velocity of 21.3 m / s ):

The theoretical kinetic energy gain by sliding down a frictionless slide is KE = ( 1 / 2 )( 70 kg )( 21.3 m / s^2) = 15,897 J, or 15.9 kJ.

You'll get good practice by working the rest of the problem. Convert ( 38.2 m / h ) to ( m / s ). After you get a value of ( v ) in metric units, plug this value into the KE = ( 1 / 2 )( m )( v^2 ) equation. Finally, subtract the value of KE that you derive from the theoretical value of KE obtained by sliding down a frictionless surface. KE theoretical - KE actual = Energy lost to friction.

Lastly, the question asks for the force of friction ( Ff ). The S.I. unit of force ( F ) is the Newton ( N ). It takes energy ( J ) to do work, and the equation of Work ( J ) = ( F )( d ), where F = force, and d = distance. Therefore, ( Energy lost to friction ) / ( d ) = Force of friction ( Ff ). Take the value of the energy lost to friction and divide it by the length of the slide ( 27.4 m ).

Best of luck in your studies!