Answer:
a= Vo²/(2X₁)
Fr= mVo²/(2X₁)
Explanation:
Given that
Initial velocity = Vo
As we know that friction always tried to oppose the motion of the object.That is why acceleration due to friction acts opposite to the motion of the object.Lets take acceleration is a.
We also know that
v²=u²+ 2 a s
v=final speed
u=initial speed
a= acceleration
s= distance
Here given that final speed is zero.
So
0²=Vo² - 2 x a x X₁ ( negative sign because acceleration in the opposite to the displacement)
a= Vo²/(2X₁)
So the average friction force Fr
Fr= m a
Fr= mVo²/(2X₁)
Answer:
Part a)

Part b)

Part c)

Part d)

Part e)

Part f)

Explanation:
Part a)
As we know that the maximum angle deflected by the pendulum is

so the maximum height reached by the pendulum is given as

so we will have



now gravitational potential energy of the pendulum is given as



Part b)
As we know that there is no energy loss while moving upwards after being stuck
so here we can use mechanical energy conservation law
so we have




Part c)
now by momentum conservation we can say



Part d)
Work done by the bullet is equal to the change in kinetic energy of the system
so we have



Part e)
recoil speed of the gun can be calculated by momentum conservation
so we will have



Part f)
Total energy released in the process of shooting of gun



Answer:
The woman's distance from the right end is 1.6m = (8-6.4)m.
The principles of moments about a point or axis running through a point and summation of forces have been used to calculate the required variable.
Principle of moments: the sun of clockwise moments must be equal to the sun of anticlockwise moments.
Also the sun of upward forces must be equal to the sun of downward forces.
Theses are the conditions for static equilibrium.
Explanation:
The step by step solution can be found in the attachment below.
Thank you for reading this solution and I hope it is helpful to you.
The average speed would have to be 260 km/hr due to the driver originally going 30 km/hr too slow the first two laps
Not 100% but i think it'll cause the earth to rotate slightly slower, its definitely not the last one though