A bowling ball weighing 71.2 N is attached to the ceiling by a 3.80 m rope. The ball is pulled to one side and released; it then swings back and forth like a pedulum. as the rope swings through its lowest point, the speed of the bowling ball is measured at 4.20 m/s. At that instant, find a) the magnitude and direction of the acceleration of the bowling ball and b) the tension in the rope.

a) The magnitude of the acceleration is V^2/R and it is directed along the rope (i.e. vertical), perpendicular to the direction of motion.

b) If the rope tension is T, Newton's Second Law tells you that

F = T - Mg = Ma = M V^2/R

Solve for T

T = M*(g + V*2/R)

R is the rope length.

Bread

thanks

Since it's a pendulum, we we'll use the formula for circular acceleration.

Therefore; a=v^/r
a=v^2/r
=(4.2)^2/3.8
=4.64m/s^2
Since the circular acceleration is always directed to the center so the acceleration of the bowling ball is directed to the center.

b) To find the tension, first we have to find the mass using F=ma.
F=ma
71.2=m(9.81)
m=7.23kg
We cannot use the acceleration to be 9.81, instead we'll use (9.81- 4.64)
Weight of the swinging pendulum=Force=ma=(7.23)(9.81- 4.64)=37.5N

*Now we’ll use Newton’s second law;
T-mg=ma
T-(7.23)(9.81)=(7.23)(9.81-4.46)
T-71.2=(7.23)(5.17)
T-71.2=37.5
T=37.5+71.2
T=108.7N

There's two of my answers above so chose whichever you prefer

To find the magnitude and direction of the acceleration of the bowling ball, we can use the equation for the acceleration of an object in simple harmonic motion (SHM):

a = -(ω^2) * x

where a is the acceleration, ω is the angular frequency, and x is the displacement from the equilibrium position. In this case, the equilibrium position is when the rope is vertical, and x is the distance from the lowest point of the swing (where the speed is measured).

First, we need to find the angular frequency (ω). The angular frequency is related to the period (T) of the pendulum by the equation ω = 2π / T. The period of a pendulum is the time it takes for one complete swing back and forth.

To find T, we need to use the relationship between the length of the pendulum (L) and the period. For small angles of displacement, the period of a simple pendulum is given by T = 2π * √(L / g), where g is the acceleration due to gravity (approximately 9.8 m/s^2).

In this case, the length of the pendulum is the length of the rope, which is 3.80 m. Plugging this value into the equation, we have:

T = 2π * √(3.80 / 9.8)

Calculating this expression gives us the period T.

Once we have the period, we can calculate the angular frequency ω using the equation ω = 2π / T.

Now that we have ω and x, we can substitute them into the equation for acceleration:

a = -(ω^2) * x

This will give us the magnitude and direction of the acceleration of the bowling ball at the lowest point of the swing.

To find the tension in the rope, we can use the centripetal force equation:

F = m * a

where F is the tension in the rope, m is the mass of the bowling ball, and a is the acceleration of the bowling ball.

In this case, the mass of the bowling ball is not given directly, but we can use the weight of the ball to find it. Weight (W) is given by the equation W = m * g, where g is the acceleration due to gravity.

To find the tension in the rope, we need to substitute the mass of the bowling ball and the acceleration into the equation for centripetal force:

F = m * a

This will give us the tension in the rope at the lowest point of the swing.

By following this process, you should be able to find the answers to both parts (a) and (b) of the question.

So for a I got 17.64 / 3.80 = 4.64 sec is this correct

and then for b i got 71.2( 9.8+ 4.20)*2 / 3.80 and got 524.63

hell naw

LMBO!!!

Since it's a pendulum, we we'll use the formula for circular acceleration.

Therefore; a=v^/r
a=v^2/r
=(4.2)^2/3.8
=4.64m/s^2
Since the circular acceleration is always directed to the center so the acceleration of the bowling ball is directed to the center.

b) To find the tension, first we have to find the mass using F=ma.
F=ma
71.2=m(9.81)
m=7.23kg
We cannot use the acceleration to be 9.81, instead we'll use (9.81- 4.64)
Tension=Force=ma=(7.23)(9.81- 4.64)=37.5N