Initially, the system of objects shown in Figure P5.49 is held motionless. The pulley and all surfaces and wheels are frictionless. Let the force
Figure P5.49 Problems 49 and 53
(a)
The tension in the string.
Answer to Problem 53CP
The tension in the string is
Explanation of Solution
Consider the free body diagram given below,
Figure I
Here,
Write the expression for the equilibrium condition for hanging block
Here,
Write the expression for the equilibrium condition for top block
Here,
Write the expression for the equilibrium condition for large block
Here,
Substitute
Further, solve for
Conclusion:
Therefore, the tension in the string is
(b)
The acceleration of
Answer to Problem 53CP
The acceleration of
Explanation of Solution
The force applied on the block of mass
Substitute
Substitute
Conclusion:
Therefore, the acceleration of
(c)
The acceleration of
Answer to Problem 53CP
The acceleration of
Explanation of Solution
The acceleration of
Substitute
Conclusion:
Therefore, the acceleration of
(d)
The acceleration of
Answer to Problem 53CP
The acceleration of
Explanation of Solution
The block of mass
Write the formula to calculate the acceleration of
Here,
Substitute
Substitute
Conclusion:
Therefore, the acceleration of
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Chapter 5 Solutions
Physics for Scientists and Engineers
- Two blocks with masses Mj and M2 are connected by a massless string that passes over a massless pulley as shown. M has a mass of 2.25 kg and is on an incline of 0 41.5° with coefficient of kinetic friction u = 0.205. M2 has a mass of 5.25 kg and is on an incline of 02 = 34.5° with coefficient M2 of kinetic friction u, = 0.105. The two-block system is in M1 motion with the block of mass M2 sliding down the ramp. Find the magnitude az of the acceleration of M, down the incline. Figure is not to scale. a2 = m/s?arrow_forwardThe 2.7-kg pendulum bob moves in the vertical plane with a velocity of 8 m/s when θ = 0∘. Neglect the size of the bob. (A) Determine the initial tension in the cord. Express your answer to three significant figures and include the appropriate units. (B) Determine the tension in the cord at the instant the bob reaches θθ = 30∘∘. Express your answer to three significant figures and include the appropriate units.arrow_forwardConsider a bow and arrow. Suppose the bow is held vertically, and the string is drawn back from its midpoint so the arrow is horizontal. Each half of the string makes an angle θ with the vertical, as shown in the diagram. A horizontal force with magnitude F is applied to the tail of the arrow, and the system is motionless. Write an expression for the tension, T, in the string.arrow_forward
- Consider a conical pendulum with a bob of mass m 73.0 kg on a string of length L 10.0 m that makes an angle of 04.00 with the vertical. (Consider i to be towards the center of the circular path and+J to be upward.) (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. NI+ NJ (b) Determine the radial acceleration of the bob. m/s²arrow_forwardConsider a conical pendulum with a bob of mass m = 70.0 kg on a string of length L = 10.0 m that makes an angle of ? = 6.00° with the vertical. (Consider +î to be towards the center of the circular path and +ĵ to be upward.) (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. (b) Determine the radial acceleration of the bob.arrow_forwardAs shown below, a block of mass ?1=2.50kg rests on a ramp of mass ?2=8.85kg. The ramp has an incline of ?=52.0°above the horizontal. The surface of the ramp is frictionless, and the ground on which the ramp rests is also frictionless. The ramp is not attached to the ground. The system is released from rest. (a) What is the magnitude of the acceleration of the ramp? (b) What static friction coefficient would be needed between the ramp and the floor in order to keep prevent the ramp from accelerating?arrow_forward
- An athlete pulls box E using an inextensible rope P while being resisted by another inextensible rope S. Let P be the tension force on rope P and S be the tension force on rope S. Consider particle analysis involving only forces P and S. The same athlete now pulls another box E of mass 63kg up an incline. The coefficients of friction between the box and the incline are us=0.32 and µk=0.22. Consider particle analysis of the instant when P = 635N, 0 = 10° and a = 29°. Use the indicated coordinate axes. P 4. Which of the following is closest to the friction force as the box moves up the incline? Hint: the normal force between the box and the incline is N=401.9N. 88.4 N i -125.8 N i -88.4N i -493 N iarrow_forwardAn athlete pulls box E using an inextensible rope P while being resisted by another inextensible rope S. Let P be the tension force on rope P and S be the tension force on rope S. Consider particle analysis involving only forces P and S. The same athlete now pulls another box E of mass 63kg up an incline. The coefficients of friction between the box and the incline are us=0.32 and µk=0.22. Consider particle analysis of the instant when P = 635N, 0 = 10° and a = 29°. Use the indicated coordinate axes. P 5. Which of the following is closest to the resultant of the friction force f and normal force N? 636N, 39.2deg CW from -x 422N, 72.3deg cW from -x 422 N, 77.6deg CCW from +x 411N, 77.6deg CW from -xarrow_forwardBlock A, with a mass of 13 kg, sits on an incline of 0.34 radians above the horizontal. An attached (massless) string passes through a massless, frictionless pulley at the top of the incline as shown: The coefficient of kinetic friction between block A and the incline is given as 0.47. When the system is released from rest, block B accelerates downward at 2.4 m/s2. What is the mass of block B? Express your answer in kg, to at least one digit after the decimal point.arrow_forward
- A box of mass 3.6 kg is given an initial speed of vo = 7.1 m/s along a ramp as indicated in the figure (0 = 65.5°). m If the coefficient of kinetic friction between the box and the ramp is u = 0.72, find the magnitude of the acceleration of the box. (in m/s^2)arrow_forwardAn athlete pulls box E using an inextensible rope P while being resisted by another inextensible rope S. Let P be the tension force on rope P and S be the tension force on rope S. Consider particle analysis involving only forces P and S. The same athlete now pulls another box E of mass 63kg up an incline. The coefficients of friction between the box and the incline are us=0.32 and µk=0.22. Consider particle analysis of the instant when P = 635N, 0 = 10° and a = 29°. Use the indicated coordinate axes. P 3. Which of the following is closest to the magnitude of the component of the weight PARALLEL to the incline - i.e., along x-axis? 62.0 10.94N 608N 107.3Narrow_forwardA box of mass 18.0 kgkg sits at rest on a horizontal surface. The coefficient of kinetic friction between the surface and the box is 0.300. The box is initially at rest, and then a constant force of magnitude F and direction 31.0 ∘∘ below the horizontal is applied to the box; the box slides along the surface What is F if the box has a speed of 6.00 m/sm/s after traveling a distance of 8.00 mm? What is Fb if the surface is frictionless and all the other quantities are the same? What is Fc if all the quantities are the same as in part AA but the force applied to the box is horizontal?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning