Question

1)A 75 kg cyclist races around a circular track at a constant speed of 20 m/s. The radius of the track is 50 m. Express both of your answers to the nearest whole number.

a) What is the acceleration of the cyclist?

b) What is the net force acting on the cyclist?

2)In the Bohr model of the hydrogen atom, an electron circles a proton in an orbit whose radius is 5.30 x 10^-11 m.

a) Find the magnitude of the gravitational force between the electron and the proton

b) Find the magnitude of the electrostatic force between the electron and the proton.

For both, express your answer in scientific notation, rounded to the nearest tenth.

3)Strictly speaking, Newton's law of universal gravitation, F = Gm₁m₂/r², is valid only if the masses are either point masses or __________________.

Answer 1

1)

Mass of cyclist,M=75 kg

Radius of circular path,R=50m

Velocity of cyclist,v=20 m/s

part a.

Acceleration of cyclist,a=v²/R=20²/50=8 m/s²

Part b.

Net force acting on the cyclist,F=Ma=75(8)=600 N

2)

Mass of electron,m_e=9.110^-31 kg

Mass of proton,m_p=1.6710^-27 kg

charge on each,e=1.610^-19 C

Radius of atom,R=5.3010^-11 m

According to Newton law of gravitation

Part a.

Magnitude of the gravitational force between the electron and the proton

F=Gm_em_p/R²

Where G=6.6710^-11 Nm²(kg)^-2 is gravitational constant

F=(6.6710^-119.110^-311.6710^-27 )/(5.3010^-11)²=3.610^-47 N

Part b.

Magnitude of the electrostatic force between the electron and the proton is given by

F=ke²/R²

Where k=8.9910⁹ Nm²C^-2 is electrostatic constant.

So

F=[8.9910⁹(1.610^-19)²]/(5.3010^-11)²=8.1910^-8 N

3.

Strictly speaking, Newton's law of universal gravitation, F = Gm1m2/r2, is valid only if the masses are either point masses or _Heavy masses._________________.