Concept explainers
(a)
The expression for the tension in each section of string.
(a)
Answer to Problem 50P
The expression for the tension in each section of string is
Explanation of Solution
The free body diagram for the system is given by figure 1.
Write the expression for the net force from Newton’s second law.
Here,
Conclusion:
Substitute,
Substitute,
Divide equation (IV) by (III) and substitute
Substitute,
Thus, the expression for the tension in each section of string is
(b)
The expression for the angle
(b)
Answer to Problem 50P
The expression for the angle
Explanation of Solution
Write the expression for the net force from Newton’s second law.
Conclusion:
Divide equation (IV) by (III) and substitute
Thus, the expression for the angle
(c)
The expression for the distance between the endpoints of the string.
(c)
Answer to Problem 50P
The expression for the distance between the endpoints of the string is
Explanation of Solution
Write the expression for the total length.
Here,
Write the expression for the distance.
Conclusion:
Substitute,
Thus, the expression for the distance between the endpoints of the string is
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Chapter 4 Solutions
Principles of Physics
- Two blocks, each of mass m = 3.50 kg, are hung from the ceiling of an elevator as in Figure P4.33. (a) If the elevator moves with an upward acceleration a of magnitude 1.60 m/s2, find the tensions T1 and T2 in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0 N, what maximum acceleration can the elevator have before a string breaks? Figure P4.33 Problems 33 and 34.arrow_forwardA bag of cement weighing 325 N hangs in equilibrium from three wires as suggested in Figure P4.23. Two of the wires make angles 1 = 60.0 and 2 = 40.0 with the horizontal. Assuming the system is in equilibrium, find the tensions T1, T2, and T3 in the wires. Figure P4.23 Problems 23 and 24.arrow_forwardIf the vector components of the position of a particle moving in the xy plane as a function of time are x(t)=(2.5ms2)t2i and y(t)=(5.0ms3)t3j, when is the angle between the net force on the particle and the x axis equal to 45?arrow_forward
- Two blocks, each of mass m, are hung from the ceiling of an elevator as in Figure P4.33. The elevator has an upward acceleration a. The strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b) Compare the two tensions and determine which string would break first if a is made sufficiently large. (c) What are the tensions if the cable supporting the elevator breaks? Figure P4.33 Problems 33 and 34.arrow_forwardIn the figure, block 1 of mass m1 = 1.9 kg and block 2 of mass m2 = 1.4 kg are connected by a string of negligible mass. Block 2 is pushed by force F→ of magnitude 23 N and angle θ = 33°. The coefficient of kinetic friction between each block and the horizontal surface is 0.16. What is the tension in the string?arrow_forwardFour blocks with masses m1=5.00kg, m2= 5.10kg, m3= 7.00kg, m4= 7.20kg are pulled on a horizontal, frictionless surface by a 33.0 N force that makes a 34 degree angle with the horizontal. What is the magnitude of the tension between m2 and m3 blocks?arrow_forward
- Cauchy is trying to push a cart with a force of 75N at an angle of 34 degrees, but the ground is sloped in a way that causes the cart to naturally slide with a force of 20N at an angle of 274 degrees. What direction and with what force should Cauchy actually push the cart?arrow_forwardthe coefficient of static friction between block A and a horizontal floor is 0.320, and the coefficient of static friction between block B and the floor is 0.300. The mass of each block is 2.00kg,and they are connected together by a cord. If a horizontal force F pulling on block B is slowly increased ,in a direction parallel to the connectin cord,until the block start sliding ,what is the magnitude of F at the instant that they start to slide?arrow_forwardA pig has weight 500 N. It stands on a scale in an elevator, which reads 530 N. Which is correct?A. the elevator is moving at constant velocityB. the elevator is stationaryC. the elevator is accelerating upD. the elevator is accelerating down.arrow_forward
- A jet plane is flying with a constant speed along a straight line, at an angle of 30.0° above the horizontal, as shown in part (a) of the drawing. The plane has a weight of magnitude 82300 N, and its engines provide a forward thrust . In addition, the lift force (directed perpendicular to the wings) and the force of air resistance (directed opposite to the motion) act on the plane. Part (b) of the drawing shows the free-body diagram of the plane. The air resistance has magnitude 55500 N. What are (a) the thrust and (b) the lift?arrow_forwardA ball of mass m1 = 4.0 kg and a block of mass m2 = 3.0 kg are attached by a lightweight cord that passes over a frictionless pulley of negligible mass. The block lies on an incline of angle 25o which has a coefficient of kinetic friction μk=0.20, while the ball hangs down over the pulley. As the block slides up the incline, find: a) the magnitude of the block’s acceleration b) the tension in the cordarrow_forwardTarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0 with the vertical. Assume that an x axis extends horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 760 N. Just then, what are (a) the force on him from the vine in unit-vector notation and the net force on him (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the x axis? What are the (e) magnitude and (f) angle of Tarzan’s acceleration just then?arrow_forward
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