Problem 43
A large ice block of mass \(M=80.0 \mathrm{~kg}\) is held stationary on a frictionless ramp. The ramp is at an angle of \(\theta=\) \(36.9^{\circ}\) above the horizontal. a) If the ice block is held in place by a tangential force along the surface of the ramp (at angle \(\theta\) above the horizontal), find the magnitude of this force. b) If, instead, the ice block is held in place by a horizontal force, directed horizontally toward the center of the ice block, find the magnitude of this force.
Problem 44
-4.44 A mass \(m_{1}=20.0 \mathrm{~kg}\) on a frictionless ramp is attached to a light string. The string passes over a frictionless pulley and is attached to a hanging mass \(m_{2}\). The ramp is at an angle of \(\theta=30.0^{\circ}\) above the horizontal. \(m_{1}\) moves up the ramp uniformly (at constant speed). Find the value of \(m_{2}\)
Problem 45
-4.45 A pinata of mass \(M=8.0 \mathrm{~kg}\) is attached to a rope of negligible mass that is strung between the tops of two vertical poles. The horizontal distance between the poles is \(D=2.0 \mathrm{~m},\) and the top of the right pole is a vertical distance \(h=0.50 \mathrm{~m}\) higher than the top of the left pole. The pinata is attached to the rope at a horizontal position halfway between the two poles and at a vertical distance \(s=1.0 \mathrm{~m}\) below the top of the left pole. Find the tension in each part of the rope due to the weight of the pinata.
Problem 46
A pinata of mass \(M=12\) kg hangs on a rope of negligible mass that is strung between the tops of two vertical poles. The horizontal distance between the poles is \(D=2.0 \mathrm{~m}\), the top of the right pole is a vertical distance \(h=0.50 \mathrm{~m}\) higher than the top of the left pole, and the total length of the rope between the poles is \(L=3.0 \mathrm{~m}\). The pinata is attached to a ring, with the rope passing through the center of the ring. The ring is frictionless, so that it can slide freely
Problem 47
Three objects with masses \(m_{1}=36.5 \mathrm{~kg}, m_{2} 19.2 \mathrm{~kg},\) and \(m_{3}=12.5 \mathrm{~kg}\) are hanging from ropes that run over pulleys. What is the acceleration of \(m_{1} ?\)
Problem 48
A rectangular block of width \(w=116.5 \mathrm{~cm},\) depth \(d=164.8 \mathrm{~cm}\) and height \(h=105.1 \mathrm{~cm}\) is cut diagonally from one upper corner to the opposing lower corners so that a triangular surface is generated, as shown in the figure. A paperweight of mass \(m=16.93 \mathrm{~kg}\) is sliding down the incline without friction. What is the magnitude of the acceleration that the paperweight experiences?
Problem 49
\- 4.49 A large cubical block of ice of mass \(M=64 \mathrm{~kg}\) and sides of length \(L=0.40 \mathrm{~m}\) is held stationary on a frictionless ramp. The ramp is at an angle of \(\theta=26^{\circ}\) above the horizontal. The ice cube is held in place by a rope of negligible mass and length \(l=1.6 \mathrm{~m}\). The rope is attached to the surface of the ramp and to the upper edge of the ice cube, a distance \(I\) above the surface of the ramp. Find the tension in the rope.
Problem 50
A bowling ball of mass \(M_{1}=6.0 \mathrm{~kg}\) is initially at rest on the sloped side of a wedge of mass \(M_{2}=9.0 \mathrm{~kg}\) that is on a frictionless horizontal floor. The side of the wedge is sloped at an angle of \(\theta=36.9^{\circ}\) above the horizontal. a) With what magnitude of horizontal force should the wedge be pushed to keep the bowling ball at a constant height on the slope? b) What is the magnitude of the acceleration of the wedge, if no external force is applied?
Problem 51
A skydiver of mass \(82.3 \mathrm{~kg}\) (including outfit and equipment) floats downward suspended from her parachute, having reached terminal speed. The drag coefficient is 0.533 , and the area of her parachute is \(20.11 \mathrm{~m}^{2} .\) The density of air is \(1.14 \mathrm{~kg} / \mathrm{m}^{3}\). What is the air's drag force on her?
Problem 52
The elapsed time for a top fuel dragster to start from rest and travel in a straight line a distance of \(\frac{1}{4}\) mile \((402 \mathrm{~m})\) is 4.41 s. Find the minimum coefficient of friction between the tires and the track needed to achieve this result. (Note that the minimum coefficient of friction is found from the simplifying assumption that the dragster accelerates with constant
