University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 7, Problem 7.33E
CALC A small block with mass 0.0400 kg is moving in the xy-plane. The net force on the block is described by the potential- energy function U(x, y) = (5.80 J/m2)x2 − (3.60 J/m3)y3. What are the magnitude and direction of the acceleration of the block when it is at the point (x = 0.300 m, y = 0.600 m)?
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Chapter 7 Solutions
University Physics (14th Edition)
Ch. 7 - A baseball is thrown straight up with initial...Ch. 7 - A projectile has the same initial kinetic energy...Ch. 7 - An object is released from rest at the top of a...Ch. 7 - An egg is released from rest from the roof of a...Ch. 7 - A physics teacher had a howling hall suspended...Ch. 7 - Is it possible for a friction force to increase...Ch. 7 - A woman bounces on a trampoline, going a little...Ch. 7 - Q7.8 Fractured Physics. People often call their...Ch. 7 - (a) A book is lifted upward a vertical distance of...Ch. 7 - (a) A block of wood is pushed against a spring,...
Ch. 7 - A 1.0-kg stone and a 10.0-kg stone are released...Ch. 7 - Two objects with different masses are launched...Ch. 7 - When people are cold, they often rub their hands...Ch. 7 - A box slides down a ramp and work is done on the...Ch. 7 - In physical terms, explain why friction is a...Ch. 7 - Since only changes in potential energy are...Ch. 7 - Figure 7.22a shows the potential-energy function...Ch. 7 - Figure 7.22b shows the potential-energy function...Ch. 7 - For a system of two particles we often let the...Ch. 7 - Explain why the points x = A and x = A in Fig....Ch. 7 - A particle is in neutral equilibrium if the net...Ch. 7 - The net force on a particle of mass m has the...Ch. 7 - The potential-energy function for a force F is...Ch. 7 - In one day, a 75-kg mountain climber ascends from...Ch. 7 - BIO How High Can We Jump? The maximum height a...Ch. 7 - CP A 90.0-kg mail bag hangs by a vertical rope 3.5...Ch. 7 - BIO Food Calories. The food calorie, equal to 4186...Ch. 7 - A baseball is thrown from the roof of a...Ch. 7 - A crate of mass M starts from rest at the top of a...Ch. 7 - BIO Human Energy vs. Insect Energy. For its size,...Ch. 7 - Prob. 7.8ECh. 7 - Prob. 7.9ECh. 7 - A 25.0-kg child plays on a swing having support...Ch. 7 - You are testing a new amusement park roller...Ch. 7 - Tarzan and Jane. Tarzan, in one tree, sights Jane...Ch. 7 - CP A 10.0-kg microwave oven is pushed 6.00 m up...Ch. 7 - An ideal spring of negligible mass is 12.00 cm...Ch. 7 - A force of 520 N keeps a certain spring stretched...Ch. 7 - BIO Tendons. Tendons are strong elastic fibers...Ch. 7 - A spring stores potential energy U0 when it is...Ch. 7 - A slingshot will shoot a 10-g pebble 22.0 m...Ch. 7 - A spring of negligible mass has force constant k =...Ch. 7 - A 1.20-kg piece of cheese is placed on a vertical...Ch. 7 - A spring of negligible mass has force constant k =...Ch. 7 - (a) For the elevator of Example 7.9 (Section 7.2),...Ch. 7 - A 2.50-kg mass is pushed against a horizontal...Ch. 7 - A 2.50-kg block on a horizontal floor is attached...Ch. 7 - You are asked to design a spring that will give a...Ch. 7 - A 75-kg roofer climbs a vertical 7.0-m ladder to...Ch. 7 - A 0.60-kg book slides on a horizontal table. The...Ch. 7 - CALC In an experiment, one of the forces exerted...Ch. 7 - A 62.0-kg skier is moving at 6.50 m/s on a...Ch. 7 - Prob. 7.30ECh. 7 - CALC A force parallel to the .v-axis acts on a...Ch. 7 - CALC The potential energy of a pair of hydrogen...Ch. 7 - CALC A small block with mass 0.0400 kg is moving...Ch. 7 - CALC An object moving in the xy-plane is acted on...Ch. 7 - CALC The potential energy of two atoms in a...Ch. 7 - A marble moves along the x-axis. The...Ch. 7 - At a construction site, a 65.0-kg bucket of...Ch. 7 - Two blocks with different masses are attached to...Ch. 7 - A block with mass 0.50 kg is forced against a...Ch. 7 - A 2.00-kg block is pushed against a spring with...Ch. 7 - A 2.00-kg block is pushed against a spring with...Ch. 7 - CP Riding a Loop-the- Loop. A car in an amusement...Ch. 7 - A 2.0-kg piece of wood slides on a curved surface...Ch. 7 - Up and Down the Hill. A 28-kg rock approaches the...Ch. 7 - A 15.0-kg stone slides down a snow-covered hill...Ch. 7 - CP A 2.8-kg block slides over the smooth, icy hill...Ch. 7 - Bungee Jump. A bungee cord is 30.0 m long and,...Ch. 7 - You are designing a delivery ramp for crates...Ch. 7 - The Great Sandini is a 60-kg circus performer who...Ch. 7 - A 1500-kg rocket is to be launched with an initial...Ch. 7 - A system of two paint buckets connected by a...Ch. 7 - These results are from a computer simulation for a...Ch. 7 - CP A 0.300-kg potato is tied to a string with...Ch. 7 - A 60.0-kg skier starts from rest at the top of a...Ch. 7 - Prob. 7.55PCh. 7 - A ball is thrown upward with an initial velocity...Ch. 7 - Prob. 7.57PCh. 7 - A truck with mass m has a brake failure while...Ch. 7 - CALC A certain spring found not to obey Hookes law...Ch. 7 - CP A sled with rider having a combined mass of 125...Ch. 7 - CALC A conservative force F is in the +x-direction...Ch. 7 - A 3.00-kg block is connected to two ideal...Ch. 7 - A 0.150-kg block of ice is placed against a...Ch. 7 - If a fish is attached to a vertical spring and...Ch. 7 - CALC You are an industrial engineer with a...Ch. 7 - A basket of negligible weight hangs from a...Ch. 7 - CALC A 3.00-kg fish is attached to the lower end...Ch. 7 - You are designing an amusement park ride. A cart...Ch. 7 - A 0.500-kg block, attached to a spring with length...Ch. 7 - CP A small block with mass 0.0400 kg slides in a...Ch. 7 - CP A small block with mass 0.0500 kg slides in a...Ch. 7 - CP Pendulum. A small rock with mass 0.12 kg is...Ch. 7 - A wooden block with mass 1.50 kg is placed against...Ch. 7 - CALC A small object with mass m = 0.0900 kg moves...Ch. 7 - CALC A cutting tool under microprocessor control...Ch. 7 - A particle moves along the x-axis while acted on...Ch. 7 - Prob. 7.77PCh. 7 - DATA A long ramp made of cast iron is sloped at a...Ch. 7 - DATA A single conservative force F(x) acts on a...Ch. 7 - CALC A proton with mass m moves in one dimension....Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...
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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 particle is subject to a force Fx that varies with position as shown in Figure P7.9. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x = 10.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x = 0 to x = 15.0 m?arrow_forwardA large cruise ship of mass 6.50 107 kg has a speed of 12.0 m/s at some instant. (a) What is the ships kinetic energy at this time? (b) How much work is required to stop it? (c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 2.50 km?arrow_forward
- A block of mass 200 g is attached at the end of a massless spring of spring constant 50 N/m. The other end of the spring is attached to the ceiling and the mass is released at a height considered to be where the gravitational potential energy is zero. (a) What is the net potential energy of the block at the instant the block is at the lowest point? (b) What is the net potential energy of the block at the midpoint of its descent? (c) What is the speed of the block at the midpoint of its descent?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_forwardThe force acting on a particle is Fx = (8x 16), where F is in newtons anti x is in meters. (a) Make a plot of this force versus x from x = 0 to x = 3.00 m. (b) From your graph, find the net work done by this force on the particle as it moves from x = 0 to x = 3.00 m.arrow_forward(a) A force F=(4xi+3yj), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x direction from the origin to x = 5.00 m. Find the work W=Fdr done by the force on the object. (b) What If? Find the work W=Fdr done by the force on the object if it moves from the origin to (5.00 m, 5.00 m) along a straightline path making an angle of 45.0 with the positive x axis. Is the work done by this force dependent on the path taken between the initial and final points?arrow_forward
- A 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_forwardAn object of mass m = 5.8 kg moves under the influence of one force. That force causes the object to move along a path given by x = 6.0 + 5.0t + 2.0t2, where x is in meters and t is in seconds. Calculate the work done by the force on the object from t = 2.0 s to t = 7.0 s.arrow_forwardA 4.00-kg particle moves from the origin to position , having coordinates x = 5.00 m and y = 5.00 m (Fig. P7.31). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 7.3, calculate the work done by the gravitational force on the particle as it goes from O to along (a) the purple path, (b) the red path, and (c) the blue path, (d) Your results should all be identical. Why? Figure P7.31arrow_forward
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