Question

In: Physics

Figure 8-31 shows a ball with mass m ? 0.341 kg attached to the end of...

Figure 8-31 shows a ball with mass m ? 0.341 kg attached to the end of a thin rod with length L ? 0.452 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there. How much work is done on the ball by the gravitational force from the initial point to (a) the lowest point, (b) the highest point, and (c) the point on the right level with the initial point? If the gravitational potential energy of the ball–Earth system is taken to be zero at the initial point, what is it when the ball reaches (d) the lowest point, (e) the highest point, and (f) the point on the right level with the initial point? (g) Suppose the rod were pushed harder so that the ball passed through the highest point with a nonzero speed. Would ?Ug from the lowest point to the highest point then be greater than, less than, or the same as it was when the ball stopped at the highest point?

Expert Solution

The main point to be kept in mind while solving this problem is that gravity is a conservative force and only depends on the initial and final position of the object.

a) the lowest point

The work done by the gravity will be

b) the highest point

Since the motion is in the opposite direction, the work done will be negative

c) the point on the right level with the initial point

Since the vertical displacement is zero, the work done by gravity is zero.

The gravity potential energy at

d) the lowest point

The gravitational potential energy will be the negative of the work done by gravity.

Therefore, here it will be

e) the highest point

Here, it will be

f) the point on the right level with the initial point

Here, it will be zero

Suppose the rod were pushed harder so that the ball passed through the highest point with a nonzero speed. Would from the lowest point to the highest point then be greater than, less than, or the same as it was when the ball stopped at the highest point?

The depends on the height( or vertical displacement) only. Therefore, at a given height, it will be the same regardless of the speed.

genius_generous answered 2 years ago

A box of mass m = 10.0 kg is attached to a rope. The other end...

A box of mass m = 10.0 kg is attached to a rope. The other end of the rope is wrapped around a pulley with a radius of 15.0 cm. When you release the box, it begins to fall and the rope around the pulley begins to unwind, causing the pulley to rotate. As the box falls, the rope does not slip as it unwinds from the pulley. If the box is traveling at a speed of 2.50 m/s after...

A mass, m=1.4 kg of negligible size, is attached at the end of a uniform rod...

A mass, m=1.4 kg of negligible size, is attached at the end of a uniform rod of length L= 0.99 mm which has mass M= 1.9 kg . What is the moment of inertia of this arrangement if it is to rotate at an axis located at a distance 0.39*L from the end of the rod opposite to the mass, m? (At approximately the point marked with an 'X'.) Calculate the moment of inertia of the rod-mass system given that...

The figure below shows a bar of mass m = 0.220 kg that can slide without...

The figure below shows a bar of mass m = 0.220 kg that can slide without friction on a pair of rails separated by a distance script l = 1.20 m and located on an inclined plane that makes an angle θ = 34.0° with respect to the ground. The resistance of the resistor is R = 1.20 Ω and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire...

The figure below shows a bar of mass m = 0.240 kg that can slide without...

The figure below shows a bar of mass m = 0.240 kg that can slide without friction on a pair of rails separated by a distance = 1.20 m and located on an inclined plane that makes an angle θ = 29.0° with respect to the ground. The resistance of the resistor is R = 2.20 Ω and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through...

1.A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a...

1.A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum linear speed can the mass have if the string is not to break? A.370 m/s B.22 m/s C.19 m/s D.29 m/s 2.A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s2. What is the angular speed of the wheel?...

A 3-kg mass is attached to the end of a coil spring with stiffness k=48N/m ....

A 3-kg mass is attached to the end of a coil spring with stiffness k=48N/m . The mass is then pulled down 0.5m (from its equilibrium position) and released at t = 0 with an initial velocity of 2 m/sec directed upward. Neglect the resistance of the medium. a) Determine the resulting displacement and velocity as functions of time. b) Find amplitude, period and frequency of the motion. c) At what time does the weight first pass through the equilibrium...

A small metal ball with a mass of m = 97.6 g is attached to a...

A small metal ball with a mass of m = 97.6 g is attached to a string of length l = 1.43 m. It is held at an angle of θ = 42.1° with respect to the vertical. The ball is then released. When the rope is vertical, the ball collides head-on and perfectly elastically with an identical ball originally at rest. This second ball flies off with a horizontal initial velocity from a height of h = 3.26 m,...

A ball of mass m is attached to a string of length L. It is swung...

A ball of mass m is attached to a string of length L. It is swung in a vertical circle with enough speed to keep the string taut throughout the motion. Assume the ball travels freely in the circle with negligible loss of mechanical energy. Determine if the following six statements are true or false; e.g., enter TTFFFF. The tension in the string is less at the top of the circle than at the bottom of the circle. The acceleration...

A block with mass 5 kg is attached to the end of a horizontal spring with...

A block with mass 5 kg is attached to the end of a horizontal spring with spring constant 200N/m. The other end of the spring is attached to a wall. The spring is stretched 10cm in the positive directions from its equilibrium length. Assume that the block is resting on a frictionless surface. A) When the spring is fully stretched, what is the magnitude of the force from the spring on the block? B) We then release the block, letting...

Suppose a 1 kg mass is attached to the end of a string that is stretched...

Suppose a 1 kg mass is attached to the end of a string that is stretched 0.2 m by a force of 500 N (newtons). An exterior force F0 cos 50t acts on the mass. Find the position function x(t) if the initial conditions are given by x(0) = 0, x′(0) = 50.