A box of mass m rests on a horizontal table The coefficient of static friction is s A force F is applied at an angle as shown in Problem 5 32 (a) Find the force F needed to move the box as a function of angle (b) At the angle for which this force is minimum, the slope dF d of the curve F versus is zero Compute dF d and show that this derivative is zero at the angle that obeys tan s Compare this general result with that obtained in Problem 5 32

Question: A box of mass m rests on a horizontal table. The coefficient of static friction is s . A force F is applied at

A box of mass m rests on a horizontal table. The coefficient of static friction is µ_s. A force F is applied at an angle θ as shown in Problem 5-32.

(a) Find the force F needed to move the box as a function of angle θ.

(b) At the angle θ for which this force is minimum, the slope dF/dθ of the curve F versus θ is zero. Compute dF/dθ and show that this derivative is zero at the angle θ that obeys tan θ = µ_s. Compare this general result with that obtained in Problem 5-32.

Step by Step Solution

★★★★★

3.34 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The expression for F was obtained previously F s m gcos ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

10-P-M-L-M (619).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

A body of mass m rests on a horizontal plane with the friction coefficient k. At the moment t = 0 a horizontal force is applied to it, which varies with time as F = at, where a is a constant vector....

A block of mass m rests on a horizontal surface (figure). The block is pulled by a massless rope with a force at an angle . The coefficient of static friction is 0.6. The minimum value of the force...

A uniform solid cylinder of mass m rests on two horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force F (Fig. 1.62).Find...

Exhibit 6-1 Consider the continuous random variable x , which has a uniform distribution over the interval from 20 to 28. Refer to Exhibit 6-1. The variance of x is approximately _____. a. 2.309 b....

Can you help me with 1,4,7,9 ? specially with 4 I didn't get that at all impend if the force applied to the block is (a) horizontal and (b) upward at an angle of 20" with the horizontal. 6.9...

(10%) Problem 2: A block with a mass of m = 1.5 kg rests on a wooden plank. The coe'icient of static friction between the block and the plank is u; = I9. .78. One end of the board is attached to a...

I only need 4- B,C,D and 5- D,E and all parts for 6 AP Physics 1 U4 - WS3 - Friction Unit 4 - Forces & Acceleration page 1 11/13/2018 1. A block weighing w is moved at constant speed v over a...

Kolsawala (alk472) - 2-PHY317k-Homework - lang - (57345) is an avalanche, in which a large mass of snow 2. 1.215-44 and ice breaks loose and goes on an essentially 3. 1.36112 frictionless "ride" down...

Clearly hand.wri/te and show all steps 12. A 40-kg crate is being lowered with a downward acceleration is 2.0 m/s2 by means of a rope. (a) What is the magnitude of the force exerted by the rope on...

A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (a) If no...

Ethics is often an integral part of internal controls. Read the case study presented below and then answer the questions using the ethical analysis framework that we referred to throughout the...

In an interview for an upcoming documentary on the state of the environment colorado farmer, Pamela Bliss concluded that there is no such thing as global warming. In defending her position, Bliss...

What type of segmentation divides consumers based on personality, values, and lifestyle?

The following information was taken from the statement of financial position of Blanche Corporation: Cash Accounts Receivable (net) Merchandise Inventory P13,250 33,000 40,000 9,950 25,200 1,800...

Using the financial statement data provided in Exhibits 2, 3, and 4, match the companies with their industry. I Since oppornunities and constraints tend to be different across industries, companies...

CARLIN: Has been renting a two-bedroom apartment with her husband and 3 kids; wants to move into a three-bedroom home instead Took her five years, but she has saved $20,000 for a down payment ...

1 . Consider an all-equity financed firm. The firm has a beta of 1.1, the risk-free rate is 2%, and the market risk premium is 4%. What is the firm's WACC? (Assume the CAPM holds.) 2 . Consider a...

Youve recently been hired as an analyst for ToolPro, which manufactures four products: lawnmowers, leaf blowers, snow blowers, and generators. Your first assignment is to recommend a production plan...

If the world price of copper exceeds the domestic (U.S.) price of copper, we would expect (A) the United States to be a net exporter of copper. (B) the United States to impose a tariff on imported...

Studies of the relationship of the Sun to its galaxythe Milky Wayhave revealed that the Sun is located near the outer edge of the galactic disk, about 30 000 light-years from the center. The Sun has...

The oldest artificial satellite in orbit is Vanguard I, launched March 3, 1958. Its mass is 1.60 kg. In its initial orbit, its minimum distance from the center of the Earth was 7.02 Mm, and its speed...

Astronomers detect a distant meteoroid moving along a straight line that, if extended, would pass at a distance 3RE from the center of the Earth, where RE is the radius of the Earth. What minimum...

Suppose you own 64,000 shares of common stock in a firm with 3.2 million total shares outstanding. The firm announces a plan to sell an additional 1.6 million shares through a rights offering. The...

choice question A shortage of water in California is the result of a. global warming b greedy city dwellers irresponsibly using too much water c. the political power of farmers to obtain water...

#47 Allen Lumber Company had earnings after taxes of $570, 000 in the year 2009 with 430, 000 shares outstanding on December 31, 2009 On January 1, 2010, the firm issued 38,000 new shares. Because of...