RECITATION
CHAPTER 5
APPLICATIONS OF NEWTON’S LAWS
5.3. Two 25.0N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain that is fastened to the ceiling. (See the figure.) Start solving this problem by making a free-body diagram of each weight.
(a) What is the tension in the rope? (b) What is the tension in the chain?
For each object a = 0. Applyto each weight and to the pulley. Takeupward to be the +ydirection. The pulley has negligible mass. Let be the tension in the rope and let be the tension in the chain.
(a) the free-body diagram for each weight is the same and is given here
gives.
(b) The free-body diagram for the pulley is given here
5-12In a rescue, the 73 kg police officer is suspended by two cables, as shown in the figure below. (a) Sketch a free-body diagram of him. (b) Find the tension in each cable.
(a) Following is the free body diagram.
(b) gives
gives
Solving for T1 we get,
5.13. A tetherball leans against the smooth, frictionless post to which it is attached. (See the figure) The string is attached to the ball such that a line along the string passes through the center of the ball. The string is 1.40m long and the ball has a radius of 0.110m with mass 0.270kg. (a) Make a free body diagram of the ball. b) What is the tension in the rope?
(c) What is the force the pole exerts on the ball?
Apply to the ball. Since the post is frictionless, the force it exerts on the ball is a horizontal normal force. Use coordinates with +y upward and +x to the right.
l is the length of the string and r is the radius of the ball.
(a) The free-body diagram of the ball is given above in the figure.
(b)
(c)
5-15Two blocks, each with weight w, are held in place on a frictionless incline as shown in the figure. In terms of w and the angle of the incline, calculate the tension in (a) the rope connecting the blocks and (b) the rope that connects block A to the wall. (c) Calculate the magnitude of the force that the incline exerts on each block. Interpret your answers for the cases
When choosing a coordinate system for an inclined surface, it is generally best to have the x and y axis of the system parallel and perpendicular to the surface respectively. One can imagine the coordinate system to be “bolted down” to the surface, so that when the surface is tilted the coordinate system tilts along with it.
Consider the +x direction down the incline. The weight vector makes an angle with the –y axis. Suppose the tension in the rope connecting the two blocks has magnitude T1 and the tension in the rope connecting the block A to the wall has a magnitude T2 .
(a) For B,
(b) For block A, Since both
the blocks have the same weight, the x component of the weight vector for both
the blocks is the same.
(c) for each block gives
(d) For
For
5.22. A short train (an engine plus four cars) is accelerating at 1.10m/s2. The mass of each car is 38,000 kg, and each car has negligible frictional forces acting on it.
(a) What is the force of the engine on the first car? (b) What is the force of the first car on the second car? (c) What is the force of the second car on the third car? (d) And what is the force of the third car on the fourth car?
In solving this problem, note the importance of selecting the correct set of cars to isolate as your object.
Let the acceleration be in the +x direction.
(a)Apply to the four cars taken as a single object. m is the mass of one car and letbe the force the engine exerts on the first car.
gives and
(b)Apply to the last three cars taken as a single object. Letbe the
force the first car exerts on the second car.
give
(c)Apply to the last two cars taken as a single object. F3is the force that
the second carexerts on the third car. gives the force F3.
(d)Apply to the fourth car. F4 is the force that the third car exerts on the
fourth car. gives
5.33. At a construction site, a pallet of bricks is to be suspended by attaching a rope to it and connecting the other end to a couple of heavy crates on the roof of a building, as shown in the figure. The rope pulls horizontally on the lower crate, and the coefficient of static friction between the lower crate and the roof is 0.666. (a) What is the weight of the heaviest pallet of bricks that can be supported this way? Start with appropriate free-body diagrams. (b) What is the friction force on the upper crate under the conditions of part (A)?
(a)The free-body diagram for the two crates (treated as a single object) and the bricks is shown below. wc and wb represent the weights of the crates and the bricks respectively.
The system doesn’t move so the friction force exerted by the roof is static friction.
For the heaviest pallet of bricks this force has its maximum possible, .The
free-body diagram for the pallet of bricks is given in Figure (right).Solve: (a) For the
crates, gives and . Then
gives and .
For the bricks, gives and
(b) For the upper crate the only horizontal force on the crate would be friction. This crate has so and the friction force is zero.
5.35. A hockey puck leaves a player's stick with a speed of 9.9m/s and slides 32.0m before coming to rest. Find the coefficient of friction between the puck and the ice.
Use the information about the motion to find the acceleration of the puck and then use to relate a to the friction force. Take +x to be in the direction the puck is moving.
gives
gives n – mg = 0 and n = mg.
gives
.
5-36.Stopping distance of a car. (a) If the coefficient of kinetic friction between tires and dry pavement is 0.80, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 29.1 m/s (about 65 mi/h)? (b) On wet pavement, the coefficient of kinetic friction may be only 0.25. How fast should you drive on wet pavement in order to be able to stop in the same distance as in part (a)? (Note: Locking the brakes is not the safest way to stop.)
(a) gives n = mg.
gives . This equation gives
Then
(b) Solving the equation for v0xgives
5.48. A person pushes on a stationary 125 N box with 75 N at 30° below the horizontal, as shown in the figure. The coefficient of static friction between the box and the horizontal floor is 0.80. (a) Make a free body diagram of the box. (b) What is the normal force on the box? (c) What is the friction force on the box? (d) What is the largest the friction force could be? (e) The person now replaces his push with a 75 N pull at 30° above the horizontal. Find the normal force on the box in this case.
Use coordinates where +y is upward and +x is horizontal to the right. The applied force pushes to the left so the friction force is to the right.
(a) The free-body diagram is given here.
`
The applied force has been replaced by its x and y components.
(b)gives and
(c) gives and .
(d) The maximum possible static friction force is.
(e) The person now replaces his push with a 75 N pull at 30° above the horizontal. This
results in the vertical component of the pull in the upward direction resulting in less
normal force as calculated below:
. gives and.
5-73.A student attaches a series of weights to a tendon and measures the total length of the tendon for each weight. He then uses the data he has gathered to construct the graph shown in the figure, giving the weight as a function of the length of the tendon. (a) Does this tendon obey Hooke’s law? How do you know? (b) What is the force constant (in N/m) for the tendon? (c) What weight should you hang from the tendon to make it stretch by 8.0 cm from its unstretched length?
The unstretched length L0 of the tendon is 20.0 cm. The weight Wsuspended from the end of the tendon equals the force applied by the tendon.
(a)x = L - L0,so Hooke’s law says W = kx = kL - kL0. The graph of W versus L is of this form.
(b)is the slope of W versus x, so.
(c)W = k x = (50.0 N/m) (0.080m) = 4.0 N.
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