Question

In: Physics

A uniform rod of length 2.00 m and mass 5.00 kg is suspended by two ropes...

A uniform rod of length 2.00 m and mass 5.00 kg is suspended by two ropes of negligible mass. The rope at the lower end is horizontal. The rope at the upper end makes an angle φ = 30.0◦ with the vertical. φ θ

(a) Draw a free body diagram for the rod.

(b) What is the tension in the upper rope?

(c) What is the tension in the lower (horizontal) rope?

(d) What is the angle θ the rod makes with the vertical?

Expert Solution

PART (a)

PARTs (b)-(c)

Since the rod is in equilibrium, we have

From geometry

Inserting eq. (2) into (3),

or

From eq. (2),

or

PART (d)

Since the rod is in equillibrium, its net torque is zero. We will take as pivot point the lower end of the rod,

solving for

or

genius_generous answered 2 years ago

A uniform rod of mass 2.20 kg and length 2.00 m is capable ofrotating about...

A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.90 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles. At the origina of an xy-coordinate plane a rod of length labeled l rotates around it's midpoint. Attached to...

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a...

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a horizontal plane about a vertical axis on the left end of the rod. The rod is at rest when a 10.0-g bullet traveling in the horizontal plane of the rod is fired into the right end of the rod at an angle 90o with the rod. The bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after...

A uniform steel rod has mass 0.300 kg and length 40.0 cmand is horizontal. A uniform...

A uniform steel rod has mass 0.300 kg and length 40.0 cmand is horizontal. A uniform sphere with radius 8.00 cm and mass 0.700 kg is welded to one end of the bar, and a uniform sphere with radius 6.00 cm and mass 0.580 kg is welded to the other end of the bar. The centers of the rod and of each sphere all lie along a horizontal line. Part A How far is the center of gravity of the...

A thin, uniform bar of length L and mass M is suspended horizontally at rest. It...

A thin, uniform bar of length L and mass M is suspended horizontally at rest. It is suddenly released and, at the same instant, it is struck a sharp blow vertically upwards at one end – the duration of the impulse is negligibly short. (a) Explain the meaning of the equation Fnet = Macom (com stands for center of mass). If we call z the vertical direction, write an equation for zCOM(t), draw a sketch of zCOM(t) vs t, and...

A thin 1.5-m-long uniform rod with a total mass of 1650 g is suspended vertically at...

A thin 1.5-m-long uniform rod with a total mass of 1650 g is suspended vertically at the upper end. The moment of inertia of the rod in respect to the center of mass is mL2/12 (where L is the total length of the rod). A 12-g bullet is shot to the lower end of the rod and embeds there. The bullet speed before impact is 380 m/s. Calculate the amount of energy transferred to the heat during the collision.

A simple pendulum has a mass of 0.550 kg and a length of 2.00 m. It...

A simple pendulum has a mass of 0.550 kg and a length of 2.00 m. It is displaced through an angle of 11.0

A uniform beam is 5.00 m long and has a mass of 53.0 kg. The beam...

A uniform beam is 5.00 m long and has a mass of 53.0 kg. The beam is supported in a horizontal position by a hinge and a cable, with angle ? = 115°. (a) Draw all the forces acting on the beam. (b) Label the axis of rotation and the position vectors of each point of action. (c) What is the tension on the cable? (d) What are the magnitude of the vertical and horizontal forces acting on the hinge?...

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...

1. A uniform disk of mass M = 5.00 kg and radius r = 24.0 cm...

1. A uniform disk of mass M = 5.00 kg and radius r = 24.0 cm is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1.50 N · m. (a) What is the time required for the disk to reach an angular speed of 8.50 ✕ 102 rpm? (b) What is the number of revolutions through which the disk spins before reaching this angular speed? 2. A...

The uniform pole of length 5 m and mass M = 94.2 kg is placed against...

The uniform pole of length 5 m and mass M = 94.2 kg is placed against the supporting surfaces shown. If the coefficient of static friction at both A and B is 0.25. Determine the maximum angle theta (in degrees) at which the pole can be placed before it begins to slip.