1) A 1320 kg demolition ball swings at the end of a 34.3 m cable on the arc of a vertical circle. At the lowest point of the swing, the ball is moving at a speed of 3.32 m/s. Determine the tension in the cable.
F=ma
(34.3)(3.32) = 113.87
Ia this correct?
Tension= mg+mv^2/r
Yours is not correct.
so m=1320kg and v=3.32^2 but what is r and mg?
r = 34.3 m,
m•g=1320•9.8 =12936 N
v^2 =(3.32)^2 =11.02
To determine the tension in the cable, you need to consider the forces acting on the demolition ball at the lowest point of its swing. At this point, there are two important forces: gravity acting downward and tension in the cable acting toward the center of the circle.
To get the tension in the cable, you can start by calculating the gravitational force acting on the ball. The formula for gravitational force is: Fgravity = mg, where m is the mass of the ball (1320 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fgravity = (1320 kg)(9.8 m/s^2) = 12936 N
Next, you need to determine the net force acting on the ball at the lowest point of its swing. The net force is the vector sum of the tension force and the gravitational force. Since the ball is moving at a constant speed at the lowest point, the net force is equal to the centripetal force.
The centripetal force can be calculated using the formula: Fcentripetal = (mv^2) / r, where m is the mass of the ball, v is its velocity (3.32 m/s), and r is the radius of the circular path (equal to the length of the cable, 34.3 m).
Fcentripetal = (1320 kg)(3.32 m/s)^2 / 34.3 m = 408.9 N
Now, since the tension force is acting toward the center of the circle, it contributes to the centripetal force. Therefore, the net force can be written as:
Fnet = Fcentripetal = Ftension + Fgravity
Since the net force is equal to the centripetal force, you can set these two equations equal to each other and solve for the tension force:
Ftension + Fgravity = Fcentripetal
Rearranging the equation, you get:
Ftension = Fcentripetal - Fgravity
Substituting the values we calculated earlier:
Ftension = 408.9 N - 12936 N
Ftension ≈ -12527.1 N
The negative sign indicates that the tension force is acting in the opposite direction of the gravitational force. However, this doesn't make sense physically, as tension cannot be negative. Therefore, there might be a mistake in the calculations or assumptions made.
Double-check your calculations and let me know if there are any mistakes so I can help you further.