Answer:
a. The acceleration of the bowling ball is 9.5 m/s² toward the center
b. The tension in the rope is 140.24 N
Explanation:
given information:
ball weight, W = 71.2 N
the length of rope, R = 3.30 m
ball speed, v = 5.60 m/s
a. The acceleration of the bowling ball, α
α =
where
α = the acceleration
v = the speed
R = radius
thus
α =
=
= 9.5 m/s² toward the center
b. The tension in the rope?
according to the Newton's second law
ΣF = m a
where
F = force
m = mass
a = acceleration
so,
ΣF = m a
T - W = m a
T = m a + W
= (W a/g) + W
= (71.2 x 9.5/9.8) + 71.2
= 140.24 N
Answer:
7.50 m/s^2
Explanation:
The period of a pendulum is given by:
(1)
where
L = 0.600 m is the length of the pendulum
g = ? is the acceleration due to gravity
In this problem, we can find the period T. In fact, the frequency is equal to the number of oscillations per second, so:
And the period is the reciprocal of the frequency:
And by using this into eq.(1), we can find the value of g:
Answer:
5. Is greater than mg, always
Explanation:
If the cone has an inclination of angle β, the sum of forces will be:
x-axis (centripetal axis):
N*sin β = m*ax where ax is the centripetal acceleration
y-axis:
N*cos β - m*g = m*ay where ay is the vertical acceleration. If the block starts falling down, ay will be negative. If the block starts sliding up, ay will be positive. If the block does not move up nor down, ay=0.
Solving for N:
If ay is positive or zero, N will be greater than mg. If ay is negative, N will be less than mg.
If the block is sliding along a horizontal circular path (not up, nor down), ay = 0, so N will always be greater than mg.