Explanation:
Suppose the cheetah is initially positioned at x=0 (m) from the reference, and the gazelle is intially at poisiton x=d (m).
Then, at the worst case, that is when cheetah is running at the maximum case, the position of the gazelle relative to the reference must be larger than that of cheetah.
In equation form,
Answer:
Speed of 0.08 kg mass when it will reach to the bottom position is 1.94 m/s
Explanation:
When rod is released from rest then due to unbalanced torque about the hinge the system will rotate
Now moment of inertia of the system is given as
now we have
now we have
so we have
now by energy conservation we can say work done by gravity must be equal to change in kinetic energy
so we have
Now speed of 0.08 kg mass when it reaches to bottom point is given as
Answer:
a) 250 N/m
b) 22.4 rad/s , 3.6 Hz , 0.28 sec
c) 0.3125 J
Explanation:
a)
F = force applied on the spring = 7.50 N
x = stretch of the spring from relaxed length when force "F" is applied = 3 cm = 0.03 m
k = spring constant of the spring
Since the force applied causes the spring to stretch
F = k x
7.50 = k (0.03)
k = 250 N/m
b)
m = mass of the particle attached to the spring = 0.500 kg
Angular frequency of motion is given as
= 22.4 rad/s
= frequency
Angular frequency is also given as
= 2 π
22.4 = 2 (3.14) f
= 3.6 Hz
= Time period
Time period is given as
= 0.28 sec
c)
A = amplitude of motion = 5 cm = 0.05 m
Total energy of the spring-block system is given as
U = (0.5) k A²
U = (0.5) (250) (0.05)²
U = 0.3125 J