Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Q22P

Expert-verified
Physics For Scientists & Engineers
Found in: Page 238
Physics For Scientists & Engineers

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

The coefficient of friction between the block of mass m1=3.00 kgand the surface in Figure P8.22 is.μk=0.400 The system starts from rest. What is the speed of the ball of mass m2=5.00 kgwhen it has fallen a distanceh=1.5 m?

The speed of the ball when it has fallen a distance h=1.5 m isv=3.74  m/s .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Law of conservation of energy

In the presence of dissipative forces, the law of conservation of energy states that the total change in mechanical energy during a process, should be equal to the increase in internal energy of the system.

ΔEmech=ΔK+ΔUg=-fkd=-ΔEint  ...............(8.16)

If a system is not isolated as well, the total change in energy is given as-

ΔE=ΔK+ΔU+ΔEint=∑Wother forces   ............(8.17)

here,

ΔK= Change in kinetic energy

ΔU= Change in potential energy

ΔEint= Change in internal energy

Step 2: Given Data

mass of the block: m1=3.00 kg

mass of the ball: m2=5.00 kg

coefficient of friction: μk=0.400

distance moved: h=1.5 m

Step 3:

Use Equation 8.16:

ΔEmech=ΔK+ΔUg=−fkd=−ΔEint

For the system of block, ball and surface; let the subscript ‘1’ and ‘2’ denote the values of block and ball respectively. So, equation becomes-

data-custom-editor="chemistry" ΔK1+ΔU1+ΔK2+ΔU2=−fkd

Choose the initial point before release and the final point after each block have moved1.5  m . Chooseu=0 with the3.00  kg block on the tabletop and the block in its final position.

So Ki1=Ki2=U1f=U2f=Ui1=0

We now have

12m1vf2+12m2vf2+0+0−0−0−0−m2gy2i=0−fkd

where the friction force is

fk=μkn=μkmag

The friction force causes a negative change in mechanical energy because the force opposes the motion. Since all of the variables are known except for,vf we can substitute and solve for the final speed.

12m1vf2+12m2vf2−m2gy2i=−fkd

v2=2gh(m2−μkm1)m1+m2v=2(9.8 m/s2)(1.5 m)[5.00 kg-0.400(3.00 kg)]8.00  kgv=3.74 m/s

After falling 1.5 m, the ball is moving with a velocity of .3.74 m/s

Most popular questions for Physics Textbooks

Does the kinetic energy of an object depend on the frame of reference in which its motion is measured? Provide an example to prove this point.

A 10.0-kg block is released from rest at point A in Figure P8.63. The track is frictionless except for the portion between points B and C, which has a length of 6.00 m. The block travels down the track, hits a spring of force constant 2250 N/m, and compresses the spring 0.300 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between points B and C.

A 1.00-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P8.62a). The object has a speed of vi = 3.00 m/s when it makes contact with a light spring (Fig. P8.62b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Fig. P8.62c). The object is then forced toward the left by the spring (Fig. P8.62d) and continues to move in that direction beyond the spring’s unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Fig. P8.62e). Find (a) the distance of compression d, (b) the speed v at the unstretched position when the object is moving to the left (Fig. P8.62d), and (c) the distance D where the object comes to rest.

Review: The mass of a car is 1 500 kg. The shape of the car’s body is such that its aerodynamic drag coefficient is D = 0.330 and its frontal area is 2.50 m2. Assuming the drag force is proportional to v2and ignoring other sources of friction, calculate the power required to maintain a speed of 100 km/h as the car climbs a long hill sloping at 3.2o.

More than 2 300 years ago, the Greek teacher Aristotle wrote the first book called Physics. Put into more precise terminology, this passage is from the end of its Section Eta:

Let P be the power of an agent causing motion; ω, the load moved; d, the distance covered; and role="math" localid="1663592691587" Δt, the time interval required. Then (1) a power equal to P will in an interval of time equal to Δt move ω2 a distance 2d; or (2) it will move w/2 the given distance d in the time interval role="math" localid="1663592904305" Δt2. Also, if (3) the given power P moves the given load w a distance d2 in time interval Δt2, then (4) P2 will move ω2 the given distance d in the given time interval Δt.

(a) Show that Aristotle’s proportions are included in the equation, PΔt=bwd where b is proportionality constant. (b) Show that our theory of motion includes this part of Aristotle’s theory as one special case. In particular, describe a situation in which it is true, derive the equation representing Aristotle’s proportions, and determine the proportionality constant.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

Work Energy and Power

Read explanation

Radiation

Read explanation

Astrophysics

Read explanation

Fluids

Read explanation

Physics of Motion

Read explanation

Famous Physicists

Read explanation

Torque and Rotational Motion

Read explanation

Fields in Physics

Read explanation

Scientific Method Physics

Read explanation

Magnetism

Read explanation

Particle Model of Matter

Read explanation

Physical Quantities and Units

Read explanation

Medical Physics

Read explanation

Further Mechanics and Thermal Physics

Read explanation

Energy Physics

Read explanation

Force

Read explanation

Waves Physics

Read explanation

Modern Physics

Read explanation

Atoms and Radioactivity

Read explanation

Dynamics

Read explanation

Electricity and Magnetism

Read explanation

Fundamentals of Physics

Read explanation

Kinematics Physics

Read explanation

Linear Momentum

Read explanation

Geometrical and Physical Optics

Read explanation

Rotational Dynamics

Read explanation

Electrostatics

Read explanation

Space Physics

Read explanation

Magnetism and Electromagnetic Induction

Read explanation

Electromagnetism

Read explanation

Conservation of Energy and Momentum

Read explanation

Turning Points in Physics

Read explanation

Measurements

Read explanation

Engineering Physics

Read explanation

Mechanics and Materials

Read explanation

Electricity

Read explanation

Nuclear Physics

Read explanation

Circular Motion and Gravitation

Read explanation

Oscillations

Read explanation

Translational Dynamics

Read explanation

Thermodynamics

Read explanation

Electric Charge Field and Potential

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.