Two blocks are connected by a lightweight string passing over a pulley, as shown in the figure below. The block with massm1 17.5 kg on the incline plane accelerates up the plane with negligible friction. The block's acceleration is=a = 1.80 m/s², and the tension in the segment of string attached to this block is T₁. The hanging block has a mass of=m2 23.5 kg, and the tension in the string attached to it is T2. The radius of the pulley is r = 0.350 m and its moment ofinertia is I. The incline plane makes an angle of 0 = 37.0° with the horizontal.T₁T₂Ꮎm₁2(a) What is the tension force T₁? (Give your answer, in N, to at least three significant figures.)N(b) What is the tension force T2? (Give your answer, in N, to at least three significant figures.)N(c)Find a symbolic expression for the moment of inertia of the pulley in terms of the tensions T₁ and T2, the pulleyradius r, and the acceleration a. (Do not substitute numerical values; use variables only.)I =(d) What is the numerical value of the moment of inertia of the pulley? (Give your answer in kg • m².).2kg m.

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Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter5: Newton's Laws Of Motion

Section: Chapter Questions

Problem 35PQ: A black widow spider hangs motionless from a web that extends vertically from the ceiling above. If...

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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.
A 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.
For t 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet=mkv2i, where k is a constant. The speed of the object after t = 0 is given by v = vi/(1 + kvit). (a) Find the position x of the object as a function of time. (b) Find the objects velocity as a function of position.
A sleigh is being pulled horizontally by a train of horses at a constant speed of 8.05 m/s. The magnitude of the normal force exerted by the snow-covered ground on the sleigh is 6.37 103 N. a. If the coefficient of kinetic friction between the sleigh and the ground is 0.23, what is the magnitude of the kinetic friction force experienced by the sleigh? b. If the only other horizontal force exerted on the sleigh is due to the horses pulling the sleigh, what must be the magnitude of this force?
In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. Two students pull with force 196 N each to the light, four students pull with force 98 N each to the left, five students pull with force 62 N each to the left, three students pull with force 150 N each to the right, and one student pulls with force 250 N to the left. Assuming the positive direction to the tight, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction?
If a single constant force acts on an object that moves on a straight line, the objects velocity is a linear function of time. The equation v = vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object.
Why is the following situation impossible? A book sits on an inclined plane on the surface of the Earth. The angle of the plane with the horizontal is 60.0. The coefficient of kinetic friction between the book and the plane is 0.300. At time t = 0, the book is released from rest. The book then slides through a distance of 1.00 m, measured along the plane, in a time interval of 0.483 s.
A 3.00-kg object is moving in a plane, with its x and y coordinates given by x = 5t2 1 and y = 3t3 + 2, where x and y are in meters and t is in seconds. Find the magnitude of the net force acting on this object at t = 2.00 s.
If 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?
An aluminum block of mass m1 = 2.00 kg and a copper block of mass m2 = 6.00 kg are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in Figure P5.46, where = 30.0. (a) When they are released from rest, will they start to move? If they do, determine (b) their acceleration and (c) the tension in the string. If they do not move, determine (d) the sum of the magnitudes of the forces of friction acting on the blocks. Figure P5.46
In Figure P3.55, a spider is resting after starting to spin its web. The gravitational force on the spider makes it exert a downward force of 0.150 N on the junction of the three strands of silk. The junction is supported by different tension forces in the two strands above it so that the resultant force on the junction is zero. The two sloping strands are perpendicular, and we have chosen the x and y directions to be along them. The tension Tx is 0.127 N. Find (a) the tension Ty, (b) the angle the x axis makes with the horizontal, and (c) the angle the y axis makes with the horizontal.
A makeshift sign hangs by a wire that is extended over an ideal pulley and is wrapped around a large potted plant on the roof as shown in Figure P6.10. When first set up by the shopkeeper on a sunny and dry day, the sign and the pot are in equilibrium. Is it possible that the sign falls to the ground during a rainstorm while still remaining connected to the pot? What would have to be true for that to be possible? FIGURE P6.10 Problems 10 and 11.

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