A mobile at the art museum has a steel cat and a steel dog suspended from a lightweight cable, as shown in FIGURE EX It is found that when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope ?
The tension and the angle of the rope are and respectively.
Mass of the cat
Mass of dog
The horizontal component of tension in rope 1 will balance the horizontal tension in rope 2. The vertical component of tension in rope 1 will balance the weight of 2.0 kg cat.
Divide equation with equation and brings at one side as
Similarly, the second knot, which joins rope and , Horizontal component of rope 2 will balance T2 . The vertical component will balance the dog.
Substituting the given data in equation (7), we get
The tension and the angle of the rope are respectively
Your forehead can withstand a force of about before fracturing, while your cheekbone can withstand only about . Suppose a baseball traveling at strikes your head and stops in
a. What is the magnitude of the force that stops the baseball?
b. What force does the baseball exert on your head? Explain.
c. Are you in danger of a fracture if the ball hits you in the forehead? On the cheek?
A box is on a frictionless slope and is connected via a massless string over a massless, frictionless pulley to a hanging weight. The picture for this situation is similar to FIGURE P.
a. What is the tension in the string if the box is held in place, so that it cannot move?
b. If the box is then released, which way will it move on the slope?
c. What is the tension in the string once the box begins to move?
shows three hanging masses connected by massless strings over two massless, frictionless pulleys.
a. Find the acceleration constraint for this system. It is a single equation relating Hint:isn’t constant.
b. Find an expression for the tension in string Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns.
c. Suppose: Find the acceleration of each.
d. The mass would appear to be in equilibrium. Explain why it accelerates.
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