Question

A bicycle has a kinetic energy of 124 J. What kinetic energy would the bicycle have if it had … Show how you got your answer on your pdf copy. … twice the mass and was moving at the same speed? … one-half the mass and was moving with twice the speed? … three times the mass and was moving with one-half the speed? … the same mass and was moving with one-half the speed? … the same mass and was moving with twice the speed?

4)Sarah (m=45.7 kg) is traveling at a speed of 23.4 m/s at the top of a 25.0 m high roller coaster loop. Determine Sarah's speed at the bottom of the loop. Include a diagram on your pdf copy.

5)Nolan Ryan reportedly had the fastest pitch in baseball, clocked at 100.9 mi/hr (45.0 m/s) If such a pitch had been directed vertically upwards at this same speed, then to what height would it have traveled (in meters)?

Answer 1

Kinetic energy of a body with mass M and velocity v is

So,

if m' = 2m and v' = v,

SInce, KE = 124J.

KE' = 248J.

if, m' = m/2 and v' = 2v

So, KE' = 248J.

if, m' = 3m and v' = v/2

SO, KE' = 93J

if m' = m and v' = v/2

So, KE' = 31J

if m' = m and v' = 2v

So, KE' = 496J

Question 4)

Total Energy = Kinetic energy + Potential Energy

By conservation of Energy, The total energy at the top of the loop and bottom are equal.

Kinetic energy at top of the loop =

Potential energy (assuming potential is 0 at bottom of loop) at the top of loop is

So, total energy at top of loop = 23708.246J

At bottom of the loop, Total energy = KE + V =mv'^2/2 + 0

Since energy is conserved, by equating inital and final energy,

Question 5)

By equations of kinematics,

v= u + at

u = 45 m/s

a = -9.8 m/s^2

v = 0 at the top.

So,

t = 45/9.8 = 4.6 s

time required to reach top = 4.6 seconds

By another equation of kinematics,

distance travelled, s= ut + at^2/2

to get max height attained. substitute t = 4.6

s = 45*4.6 - 9.8 *4.6*4.6/2 = 103.316 m

Max height attained is 103.316m

NB: Try to ask one question with 4 subparts at most.