a simple pendulum consists of a bob of mass 1.8 kg attached to a string of length 2.3 m. the pendulum is held at an angle of 30 from the vertical by a light horizontal string attached to a wall, as shown above. calculate the tension in the horizontal string. when the horizontal string is cut, calculate the speed of the bob.

Incredible that in all these years nobody has answered you. I also had this problem and I got Tv*cos(30)=mg which solved out to 20.4N for the vertical tension and then to find the horizontal tension I did this, 20.4*sin(30)=10.4N, and so 10.4N is our horizontal tension.

As for the velocity I first solved for the height difference so (y=2.3-2.3cos(30)), then Potential energy with Pe=mgh (Pe=1.8*9.8*0.3). From there I plugged the potential energy in with kinetic energy to solve for the velocity (because Pe=Ke) so that equation would be (Ke=.5MV^2), then with the values plugged in (6=.9kg*V^2). This should solve out to 2.6 m/s.

Finally, for the period of the pendulum, our equation will look like (T=2Pi*root(L/g)) (in this case T=period, and L is of course length). Plugging in our values this equation will be something like (T=6.3*4.7) depending on how you round out which should give you a period of 2.9 seconds although again rounding will affect this a slight bit.

Anyway, I hope you can appreciate this answer 8 years late, and as for anyone else reading in the future, I hope this helps!

To calculate the tension in the horizontal string, we need to consider the forces acting on the bob of the pendulum.

When the pendulum is at rest and held at an angle of 30 degrees from the vertical, there are two forces acting on the bob: the weight force acting downward and the tension force in the horizontal string.

1. Weight Force (mg): The weight force acting on the bob is equal to the mass of the bob (m) multiplied by the acceleration due to gravity (g). In this case, the mass of the bob is 1.8 kg and the acceleration due to gravity is approximately 9.8 m/s². Therefore, the weight force is given by:
Weight Force = mass × acceleration due to gravity
= 1.8 kg × 9.8 m/s²

2. Tension Force (T): The tension force in the horizontal string is responsible for counteracting the weight force and keeping the bob at rest. As the pendulum is held at an angle, the tension force can be resolved into two components: one horizontal component and one vertical component.

- Vertical Component: The vertical component of the tension force balances the weight force and keeps the bob in equilibrium. It can be calculated using trigonometry:
Vertical Component = T × cos(angle)
= T × cos(30)

- Horizontal Component: The horizontal component of the tension force is responsible for preventing the bob from falling sideways. This is the tension force we need to calculate.
Horizontal Component = T × sin(angle)
= T × sin(30)

Since the pendulum is held at rest, the vertical component of the tension force equals the weight force:
Vertical Component = Weight Force

Now, we can solve for the tension force (T):
T × cos(30) = 1.8 kg × 9.8 m/s²

To find the speed of the bob when the horizontal string is cut, we can use the principle of conservation of energy:

The initial potential energy of the bob is converted into kinetic energy when the string is cut.

The initial potential energy is given by:
Potential Energy (PE) = mass × gravity × height
= 1.8 kg × 9.8 m/s² × 2.3 m × sin(30)

Since there is no more potential energy after cutting the string, it is converted entirely into kinetic energy:
Kinetic Energy (KE) = 1/2 × mass × velocity²

By equating the two expressions for energy, we can find the speed (velocity) of the bob:
PE = KE
1.8 kg × 9.8 m/s² × 2.3 m × sin(30) = 1/2 × 1.8 kg × velocity²

Solve the equation for velocity to find the speed of the bob when the horizontal string is cut.

its weird, bc this guy is probably like at least 27 years old LULW Weirdchamp

pos orale... contestenla que trueno la clase :(