A 6kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the string was F = ma F = (6kg * 9.8 m/s2) * 0a F = 58.8 N Now its asking At a certain point the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now? The correct answer was "about 78N"
then Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude3
m/s2.
Now what is the tension in the rope?
The concept used to solve this problem is Newton’s second law of motion.
Calculate the tension force using the Newton’s second law. The net force on the bucket is the difference of tension force pulling the bucket upwards and weight of the bucket pulling the bucket down towards the ground. Rearrange the Newton’s second law equation to calculate the tension force.
The Newton’s second law states that the net force on an object is the product of mass of the object and final acceleration of the object. The equation of the Newton’s second law is,
Here, is the net force on the object, is mass of the object, and is the acceleration of the object.
The weight of a body is the force of gravitation of the earth that is,
Here, is the weight of the body, is the mass, and is the acceleration due to gravity.
Take all the forces in upward direction as positive and all the force in downward direction as negative.
Use the Newton’s second law equation.
Two forces act on the bucket, the tension force, in the upward direction so positive and weight, in the downward direction so negative.
Substitute for in the above equation.
Use the weight equation and substitute for in the above equation and rearrange to solve for.
The acceleration of the bucket is zero when the bucket is rising at constant speed.
The expression for the tension in terms of acceleration and the acceleration due to gravity is,
Substitute for, for, and for in the above equation
The acceleration of the bucket is upward so it is positive.
Substitute for, for, and for in equation.
The acceleration of the bucket is directed in downward. So, it has negative sign. That is. Thus, the tension in the rope is,
Substitute for, for, and for.
Ans:
The tension in the rope is.
A 6kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the...
A 6-kg bucket of water is being pulled straight up by a string at a constant speed. What is the tension in the rope? A) about 42 N B) about 60 N C) about 78 N
A 14.6 kg load is pulled straight up by a massless rope from the ground to the roof of a building, at a constant acceleration of 0.81 m/s2 . During the upward motion, the tension in the rope is?
A 18.8 kgkg load is pulled straight up by a massless rope from the ground to the roof of a building, at a constant acceleration of 0.96 m/s2m/s2 . During the upward motion, the tension in the rope is
A 14.3 kg k g load is pulled straight up by a massless rope from the ground to the roof of a building, at a constant acceleration of 0.90 m/s2 m / s 2 . During the upward motion, the tension in the rope is 150 N 130 N 140 N 13 N
Two boxes connected by a string (which has tension T1) are being pulled by another string (with tension T2). The mass of box A is 450g and the mass of box B is 300 g. The floor is frictionless. If the boxes have an acceleration of 2.0 m/s2, what is the tension in each string?
(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w? T w Both forces are equal. (b) When the elevator is moving at a constant velocity upward, which is greater, T or w? T w Both forces are equal. (c) When the elevator is moving upward, but the acceleration...
2) Rita is in an elevator that is moving at a constant velocity downward. If the elevator now experiences an acceleration so that it speeds up, the normal force Rita experiences A) becomes greater than her weight. B) remains equal to her weight. C) becomes less than her weight, but not equal to zero. D) becomes zero. E) cannot be determined without more information. 11) A rope connects object A (mass 4m) with object B (mass m). (Object A is...
(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w? Tw Both forces are equal. (b) When the elevator is moving at a constant velocity upward, which is greater, T or w? Tw Both forces are equal. (c) When the elevator is moving upward, but the acceleration is downward, which is...
Use the worked example above to help you solve this problem. A solid, frictionless cylinder reel of mass M 2.60 kg and radius R = 0.397 m is used to draw water from a well (see Figure (a)). A bucket of mass m = 2.19 kg is attached to a cord that is wrapped around the cylinder. (Indicate the direction with the sign of your answer.) (a) Find the tension l' in the cord and acceleration a of the bucket....
A spool of thread, free to unwind, is on a horizontal surface (with friction) and pulled directly upward (ty) a times. The spool rolls without slipping on the floor. The spool has a mass M, moment of inertia 1, and a radius of R. Assume the string is wrapped around the spool at a radius r (where r <R). 1) Which equation below is a correct expression of Newton's Second Law (XF- ma ) in the x (hortzontal) -direction for...