Answer:
a) T = 608.22 N
b) T = 608.22 N
c) T = 682.62 N
d) T = 533.82 N
Explanation:
Given that the mass of gymnast is m = 62.0 kg
Acceleration due to gravity is g = 9.81 m/s²
Thus; The weight of the gymnast is acting downwards and tension in the string acting upwards.
So;
To calculate the tension T in the rope if the gymnast hangs motionless on the rope; we have;
T = mg
= (62.0 kg)(9.81 m/s²)
= 608.22 N
When the gymnast climbs the rope at a constant rate tension in the string is
= (62.0 kg)(9.81 m/s²)
= 608.22 N
When the gymnast climbs up the rope with an upward acceleration of magnitude
a = 1.2 m/s²
the tension in the string is T - mg = ma (Since acceleration a is upwards)
T = ma + mg
= m (a + g )
= (62.0 kg)(9.81 m/s² + 1.2 m/s²)
= (62.0 kg) (11.01 m/s²)
= 682.62 N
When the gymnast climbs up the rope with an downward acceleration of magnitude
a = 1.2 m/s² the tension in the string is mg - T = ma (Since acceleration a is downwards)
T = mg - ma
= m (g - a )
= (62.0 kg)(9.81 m/s² - 1.2 m/s²)
= (62.0 kg)(8.61 m/s²)
= 533.82 N
When talking about orbits, it would have to be a mixture of both A. and B. since Newton's first law, gravity plays a huge part in an orbit. However, the universal gravitation law also tells us the relationship between two massive objects in orbit. But to choose only one, it would have to be B. Newton's first law
Displacement is d
Vf² = Vi² + 2 g d
(-20²) = (+10²) + 2 (-9.8) d
-19.6 d = 300
d = -15.3 m
negative means lower
time is t
d = Vi t + 1/2 g t²
-15.3 = 10 t + (-4.9) t²
4.9 t² - 10 t -15.3 = 0
t = 3.06 s
Hope this helps -John
