Question

# ch 6 1: It is generally a good idea to gain an understanding of the "size"...

ch 6

1:

It is generally a good idea to gain an understanding of the "size" of units. Consider the objects and calculate the kinetic energy of each one.

.

×10

J

A 7.15 kg

bowling ball slides (not rolls) down an alley at 17.5 km/h

.

J

A car weighing 1260 kg

moves at a speed of 49.5 km/h.

5:

The graph shows the ?-directed force ?? acting on an object as a function of the position ? of the object. For each numbered interval given, find the work ??

done on the object.

1) from ?=0 m

to ?=2.70 m

?1=

J

2) from ?=3.00 m

to ?=6.10 m

?2=

J

3) from ?=7.00 m

to ?=9.30 m

?3=

J

8:

A cart for hauling ore out of a gold mine has a mass of 423 kg, including its load. The cart runs along a straight stretch of track that climbs a shallow 4.83∘ incline. A donkey, which is trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 4.30×102 N force for a distance of 127 m by means of a rope that is parallel to the slope but makes an angle of 13.9∘

with the track.

Model the rolling resistance of the cart as though it were sliding on the track with a coefficient of friction of 0.0165

. Use ?=9.81 m/s2

, and note that angle A in the image is the angle of the incline while angle B is the angle the rope makes with the track.

Find the work ?d

that the donkey performs on the cart during this process.

?d=

J

Find the work ?g

that the force of gravity performs on the cart during this process.

?g=

J

Calculate the work ?f

done on the cart by friction during this process.

?f=

J

15:

An object, which is initially at rest on a frictionless horizontal surface, is acted upon by four constant forces. ?1 is 21.6 N acting due east, ?2 is 37.0 N acting due north, ?3 is 52.1 N acting due west, and ?4 is 14.1 N acting due south. How much total work is done on the object in 3.33 s, if it has a mass of 18.0 kg

?

total work done on object:

J

Which type of energy is changing for the object while the work is being done?

gravitational potential energy

internal energy

elastic potential energy

kinetic energy

How fast does the object end up moving at the end of the 3.33 s

?

final speed of object:

18:

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height ?. The mass of each object is a multiple of the base mass ?: object 1 has mass 3.10?, object 2 has mass 1.71?, and object 3 has mass ?

. When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system?

Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some combination of the variables ?

, ?, and ?, where ? is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23???

, just enter 1.23)

??,system=

mgd

This potential energy was calculated relative to the bottom of the stairs. If you were to redefine the reference height such that the total potential energy of the system became zero, how high above the bottom of the stairs would the new reference height be?

19:

A 3 kg toy car sits at the highest point of a 13 m high hill. The car is gently pushed forward until it begins to roll down the slope. Assuming the car coasts freely, without any friction or air resistance, how much kinetic energy (KE) and potential energy (PE) will it have at each of the indicated points? Complete the diagram by placing the correct label in each bin. Use ?=10 m/s2 for the acceleration due to gravity. The diagram is not drawn to scale.

21:

Mickey, a daredevil mouse of mass 0.0187 kg, is attempting to become the world's first "mouse cannonball." He is loaded into a spring‑powered gun pointing up at some angle and is shot into the air. The gun's spring has a force constant of 72.7 N/m and is initially compressed a distance of 0.141 m

from its relaxed position.

If Mickey has a constant horizontal speed of 2.23 m/s

while he is flying through the air, how high above his initial location in the gun does Mickey soar? Assume ?=9.81 m/s2.

25:

You are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 14.3 m/s at the top of the incline, which is =37.5 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than ?=1.81 g at the top of the hump and no more than ?=5.37 g

at the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. (Figure not to scale)

What is the minimum radius ?hump

you can use for the semi-circular hump?

?hump=

27:

A child slides down a snow‑covered slope on a sled. At the top of the slope, her mother gives her a push to start her off with a speed of 0.75 m/s. The frictional force acting on the sled is one‑fifth of the combined weight of the child and the sled. If she travels for a distance of 23.0 m and her speed at the bottom is 4.15 m/s, calculate the angle ?

that the slope makes with the horizontal.

?=

28:

Starting from rest, a 29.6 kg child rides a 8.50 kg sled down a frictionless ski slope. At the bottom of the hill, her speed is 6.6 m/s. If the slope makes an angle of 16.9° with respect to the horizontal, how far along the hill did she slide on her sled?

29:

A 62.0 kg woman steps off of a diving platform with a height of 8.0 m and drops straight down into the water. If she reaches a depth of 4.9 m, what is the average magnitude of the resistance force ?average exerted on her by the water? Ignore any effects due to air resistance.

30:

A block of mass ?=3.20 kg slides along a horizontal table with velocity ?0=4.00 m/s. At ?=0, it hits a spring with spring constant ?=24.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by ?=0.300. How far has the spring compressed by the time the block first momentarily comes to rest? Assume the positive direction is to the right.

31:

Calculate the work ? done from ?=0 m to ?=5 m

by the one-dimensional force depicted in the graph.

32:

A 7.00-kg block is sent up a ramp inclined at an angle ?=30.0∘ from the horizontal. It is given an initial velocity ?0=15.0 m/s up the ramp. Between the block and the ramp, the coefficient of kinetic friction is ?k=0.30 and the coefficient of static friction is ?s=0.60.

What distance ?

along the ramp's surface does the block travel before it comes to a stop?

33:

A boy shoves his stuffed toy zebra down a frictionless chute. It starts at a height of 1.21 m above the bottom of the chute with an initial speed of 1.71 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with a coefficient of kinetic friction of 0.287. How far from the bottom of the chute does the toy zebra come to rest? Assume ?=9.81 m/s2

.

34

A tower crane has a hoist motor rated at 171 hp. If the crane is limited to using 72.0% of its maximum hoisting power for safety reasons, what is the shortest time in which the crane can lift a 5850 kg load over a distance of 77.0 m? Assume the load is lifted at a constant velocity.

35

Of waterfalls with a height of more than 50 m, Niagara Falls in Canada has the highest flow rate of any waterfall in the world. The total average flow rate of the falls is 2.80×103 m3/s and its average height is 52.0 m

(Niagara Falls Live, 2017).

Given that the density of water is 1.00×103 kg/m3

, calculate the average power output of Niagara Falls.

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