soal-soal fisika

 

Task:

1.    The escape velocity of a particle on Earth is the minimum velocity required on the Earth’s surface for the particle to escape the Earth’s gravitational field. Neglecting air resistance within the atmosphere, calculate this in terms of the Earth’s mass M and its radius R. Evaluate this numerically and show that it is close to 11 km/s.

ANSWER:

The expression for the kinetic energy of the particle is,

Here, is the mass of the particle and  is the escape velocity of the particle on the Earth.

The expression for the potential energy is,

Here,  is the gravitational constant  is the massof the earth, and  is the radius of the earth.

The initial kinetic energy of the particle is,

The initial potential  energy of the particle is,

From the law of conservation of energy , the total initial energy of the particle is equal to the total final energy of the particle.

Here ,  is the initial kinetic energy of the particle ,  is the initial potential energy of the particle ,  is the final kinetic energy of the particle , and  is the final potential energy of the particle .

When the particle escaped from the earths field, the final kinetic energy and the final potential of the particle become zero. They are  and . Thus the equation (1) becomes as follows :

Substitute  for  and  for  

Rearrange the equation for

Substitute  for G,  kg for  , and  m for .

                          

                          

Therefore, the escape velocity of the particle for the Earth is . Hence, the given statetment is proved

 

 

 

 

 

 

 

 

 

 

2.    An 80 kg man and his 10 kg parachute form a system of two particles. At one time during a descent, the forces on the parachute are the gravitational force due to the earth, a force of 720 N downward due to the man, and a force of 800 N upward due to the air. At this time, the forces on the man are the gravitational force, a force due to the parachute, and a negligible force due to the air. (a) Which of these forces are internal forces on the system? Which of them are external forces on the system? (b) What is the total internal force on the system? (c) What is the total external force on the system? Use g = 10 m/s².

ANSWER:

a.       Internal: forces exerted on man and parachute by each other. External: remaining forces.

b.      The force internal ( is zero because the internal forces on a system are just the mutual forces between particles in the system so that Similarly, the sum of any other pair of internal mutual forces is also zero. Hence the total internal force .

c.       Know:

Asked: