FUNDAMENTALS OF PHYSICS - EXTENDED
12th Edition
ISBN: 9781119773511
Author: Halliday
Publisher: WILEY
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Chapter 7, Problem 77P
(a)
To determine
To find: the work is done by the force measured by observer stationary inside the train.
(b)
To determine
To find: the work is done by the force measured by observer stationary alongside the track.
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Chapter 7 Solutions
FUNDAMENTALS OF PHYSICS - EXTENDED
Ch. 7 - Prob. 1QCh. 7 - Figure 7-16a shows two horizontal forces that act...Ch. 7 - Is positive or negative work done by a constant...Ch. 7 - Spring A is stiffer than spring B kA kB. The...Ch. 7 - In three situations, a single force acts on a...Ch. 7 - Figure 7-23 shows three arrangements of a block...Ch. 7 - SSM A proton mass m = 1.67 1027 kg is being...Ch. 7 - If a Saturn V rocket with an Apollo spacecraft...Ch. 7 - On August 10, 1972, a large meteorite skipped...Ch. 7 - An explosion at ground level leaves a crater with...
Ch. 7 - A father racing his son has half the kinetic...Ch. 7 - A ice block floating in a river is pushed through...Ch. 7 - The only force acting on a 2.0 kg canister that is...Ch. 7 - A coin slides over a frictionless plane and across...Ch. 7 - A 12.0 N force with a fixed orientation does work...Ch. 7 - A luge and its rider, with a total mass of 85 kg,...Ch. 7 - SSM WWW A helicopter lifts a 72 kg astronaut 15 m...Ch. 7 - a In 1975 the roof of Montreals Velodrome, witha...Ch. 7 - 21 SSM A cord is used to vertically lower an...Ch. 7 - A cave rescue team lifts an injured spelunker...Ch. 7 - In Fig. 7-10, we must apply a force of magnitude...Ch. 7 - During spring semester at MIT, residents of the...Ch. 7 - In Fig. 7-10a, a block of mass m lies on a...Ch. 7 - SSM WWW The only force acting on a 2.0 kg body as...Ch. 7 - SSM WWW The force on a particle is directed along...Ch. 7 - A 1.5 kg block is initially at rest on a...Ch. 7 - GO A force F= cx3.00x2iacts on a particle as the...Ch. 7 - A can of sardines is made to move along an xaxis...Ch. 7 - A single force acts on a 3.0 kg particle-like...Ch. 7 - GO Figure 7-41 shows a cord attached to a cart...Ch. 7 - SSM A force of 5.0 N acts on a 15 kg body...Ch. 7 - A skier is pulled by a towrope up a frictionless...Ch. 7 - SSM ILW A 100 kg block is pulled at a constant...Ch. 7 - The loaded cab of an elevator has a mass of 3.0 ...Ch. 7 - A machine carries a 4.0 kg package from an initial...Ch. 7 - A 0.30 kg ladle sliding on a horizontal...Ch. 7 - Prob. 49PCh. 7 - a At a certain instant, a particle-like object is...Ch. 7 - A force F= 3.00 N i 7.00 N j 7.00 N k acts on...Ch. 7 - A funny car accelerates from rest through a...Ch. 7 - SSM A horse pulls a cart with a force of 40 lb at...Ch. 7 - An initially stationary 2.0 kg object accelerates...Ch. 7 - To pull a 50 kg crate across a horizontal...Ch. 7 - A frightened child is restrained by her mother as...Ch. 7 - How much work is done by a force F= 2x N i 3 N j,...Ch. 7 - 63 SSM To push a 25.0 kg crate up a frictionless...Ch. 7 - Boxes are transported from one location to another...Ch. 7 - If a car of mass 1200 kg is moving along a highway...Ch. 7 - An iceboat is at rest on a frictionless frozen...Ch. 7 - If a ski lift raises 100 passengers averaging 660...Ch. 7 - A force F= 4.0 N i cj acts on a particle as the...Ch. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - Prob. 73PCh. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - Prob. 76PCh. 7 - Prob. 77PCh. 7 - Prob. 78P
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- A particle moves in the xy plane (Fig. P9.30) from the origin to a point having coordinates x = 7.00 m and y = 4.00 m under the influence of a force given by F=3y2+x. a. What is the work done on the particle by the force F if it moves along path 1 (shown in red)? b. What is the work done on the particle by the force F if it moves along path 2 (shown in blue)? c. What is the work done on the particle by the force F if it moves along path 3 (shown in green)? d. Is the force F conservative or nonconservative? Explain. FIGURE P9.30 In each case, the work is found using the integral of Fdr along the path (Equation 9.21). W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz) (a) The work done along path 1, we first need to integrate along dr=dxi from (0,0) to (7,0) and then along dr=dyj from (7,0) to (7,4): W1=x=0;y=0x=7;y=0(3y2i+xj)(dxi)+x=7;y=0x=7;y=4(3y2i+xj)(dyj) Performing the dot products, we get W1=x=0;y=0x=7;y=03y2dx+x=7;y=0x=7;y=4xdy Along the first part of this path, y = 0 therefore the first integral equals zero. For the second integral, x is constant and can be pulled out of the integral, and we can evaluate dy. W1=0+x=7;y=0x=7;y=4xdy=xy|x=7;y=0x=7;y=4=28J (b) The work done along path 2 is along dr=dyj from (0,0) to (0,4) and then along dr=dxi from (0,4) to (7,4): W2=x=0;y=0x=0;y=4(3y2i+xj)(dyj)+x=0;y=4x=7;y=4(3y2i+xj)(dyi) Performing the dot product, we get: W2=x=0;y=0x=0;y=4xdy+x=0;y=4x=7;y=43y2dx Along the first part of this path, x = 0. Therefore, the first integral equals zero. For the second integral, y is constant and can be pulled out of the integral, and we can evaluate dx. W2=0+3y2x|x=0;y=4x=7;y=4=336J (c) To find the work along the third path, we first write the expression for the work integral. W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz)W=rtrf(3y2dx+xdy)(1) At first glance, this appears quite simple, but we cant integrate xdy=xy like we might have above because the value of x changes as we vary y (i.e., x is a function of y.) [In parts (a) and (b), on a straight horizontal or vertical line, only x or y changes]. One approach is to parameterize both x and y as a function of another variable, say t, and write each integral in terms of only x or y. Constraining dr to be along the desired line, we can relate dx and dy: tan=dydxdy=tandxanddx=dytan(2) Now, use equation (2) in (1) to express each integral in terms of only one variable. W=x=0;y=0x=7;y=43y2dx+x=0;y=0x=7;y=4xdyW=y=0y=43y2dytan+x=0x=7xtandx We can determine the tangent of the angle, which is constant (the angle is the angle of the line with respect to the horizontal). tan=4.007.00=0.570 Insert the value of the tangent and solve the integrals. W=30.570y33|y=0y=4+0.570x22|x=0x=7W=112+14=126J (d) Since the work done is not path-independent, this is non-conservative force. Figure P9.30ANSarrow_forwardA nonconstant force is exerted on a particle as it moves in the positive direction along the x axis. Figure P9.26 shows a graph of this force Fx versus the particles position x. Find the work done by this force on the particle as the particle moves as follows. a. From xi = 0 to xf = 10.0 m b. From xi = 10.0 to xf = 20.0 m c. From xi = 0 to xf = 20.0 m FIGURE P9.26 Problems 26 and 27.arrow_forwardA shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.0° below the horizontal. (a) What is the work done on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c) What is the work done on the cart by the shopper? (d) Find the force the shopper exerts, using energy considerations. (e) What is the total work done on the cart?arrow_forward
- (a) Suppose a constant force acts on an object. The force does not vary with time or with the position or the velocity of the object. Start with the general definition for work done by a force W=ifFdr and show that the force is conservative, (b) As a special case, suppose the force F =(3i + 4j)N acts on a particle that moves from O to in Figure P7.43. Calculate the work done by F on the particle as it moves along each one of the three paths shown in the figure and show that the work done along the three paths identical.arrow_forwardConsider a particle on which a force acts that depends on the position of the particle. This force is given by . Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.arrow_forwardA force acting on a particle moving in the xy plane is given by F=(2yi+x2j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.00 m and y = 5.00 m as shown in Figure P7.31. Calculate the work done by F on the particle as it moves along (a) the purple path, (b) the red path, and (c) the blue path, (d) Is F conservative or nonconservative? (e) Explain your answer to part (d). Figure P7.31arrow_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along the x-axis from x=0 to x=5 m in some time interval. What is the work done by ?arrow_forward(a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.arrow_forward(a) Sketch a graph of the potential energy function U(x)=kx2/2+Aex2 where k , A, and are constants. (b) What is the force corresponding to this potential energy? (c) Suppose a particle of mass in moving with this potential energy has a velocity v when its position is x = . Show that the particle does not pass 2+2 through the origin unless Amv2=k22(1e a 2 ) .arrow_forward
- A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle = 25.0 below the horizontal as shown in Figure P6.3. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block. Figure P6.3arrow_forwardRepeat the preceding problem, but this time, suppose that the work done by air resistance cannot be ignored. Let the work done by the air resistance when the skier goes from A to B along the given hilly path be —2000 J. The work done by air resistance is negative since the air resistance acts in the opposite direction to the displacement. Supposing the mass of the skier is 50 kg, what is the speed of the skier at point B ?arrow_forwardGive an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.arrow_forward
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Mechanical work done (GCSE Physics); Author: Dr de Bruin's Classroom;https://www.youtube.com/watch?v=OapgRhYDMvw;License: Standard YouTube License, CC-BY