7. Granny couldn't afford to get repairs on her car, so it no longer has a functioning engine. She sits in her dead car (m = 1600 kg) at the top of a hill, at an elevation above the ground of 26.0 m, and lets it start rolling from rest. It coasts down to an elevation of 11.0 m and then continues up another hill. The top of this second hill is at an elevation of 16.0 m. What is the speed of Granny's car at the top of this second hill? Consider only conservative forces. (g = 9.81 m/s²)
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- 2. A solid cylinder (Icm = MR2/2) starts from rest, slides then rolls down a 60.0 −m high hill. The top half of the hill is covered with ice and there is no friction while the lower half is rough enough to cause the cylinder to roll without slipping. What is the translational speed of the boulder when it reaches the bottom of the hill?And don't worry about whether the passengers would actually survive the trip. They are lightweight crash test dummies. NTC A cart of mass m= 347 kg is going around a circular loop-the-loop. There is no motor. The cart moves only under the influence of gravity. Ignore friction and let g = 9.81 meters per second squared. The loop has a radius of r meters. When the cart is at the top of the loop, the normal force on the cart (exerted by the track) pushes down on the cart with a force of N = 1,330 newtons. When it is at the bottom of the loop, the cart has a speed of 30.7 meters per second. What is the radius of the loop (in units of meters)?Starting from rest at t= 0, a cyclist starts racing at constant acceleration. The wheels of the bicycle are of radius R=0.40 cm and of mass 1 kg each. The combined mass of the man and bicycle frame (without wheels) is 70 kg. When t= 10.0 s, the total kinetic energy of the cyclist and his bicycle is 4,000 J. The acceleration continues until t= 15 s, when it abruptly ceases. Through what angle does the wheel rotate in the interval t=0 to t=30 s? (Consider the wheels as hoops for the purpose of rotational inertia)
- 4. A 2.5 kg ball rolls across a frictionless surface at a velocity of 2.5m/s. It then rolls up an incline. The incline has a coefficient of kinetic friction of .12, is 1.25 m long, and has a final change in elevation of .35m. Does the ball reach the top of the incline? If so, where does the ball land? If not, what is the velocity of the ball as it rolls off the bottom of the incline? 25kg 1.25m .35mA ball of mass 2.3 kg, at one end of a string of length L=4.5 m, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball (in m/s) at the bottom of the circle is: m a. 10.50 Ob. 8.13 Oc. 9.39 Od. 14.85 Oe. 6.64The engine in a small airplane is specified to have a torque of 500 N⋅m. This engine drives a 2-m long, 40 kg single-blade propeller. On startup, how long does it take the propeller to reach 2000 rpm?
- 16. Kathy is changing the tire of her car on a steep hill 20.0 m high. She trips and drops the 10.0 kg spare tire, which rolls down the hill with initial speed of 2.00 m/s. what is the speed of the tire at the top of the next hill, which is 5.00 m high? (Ignore the effects of Rotational Kinetic Energy and friction.) *Use g=9.8 a. 18.8 m/s b. 17.3 m/s c. 12.56 m/s d. 14.6 m/s e. 16.43 m/sA point starts at a location on the x-axis and travels CCW around a circle that is centered at (0,0) at a constant angular speed. The function f(t)=24⋅sin(5t) gives the point's y-coordinate in terms of the number of seconds t since the point started moving.A tire is tied to a rope that is tied to the branch of a tree so that the tire swings in a circular trajectory of radius h1 = 15.31 m. A child takes the tire to the top of a platform that is a height h2 = 12.60 m above the ground, sits in the tire, and swings from rest from the platform. The combined mass of the tire and child is 36 kg. The rope is taut when the child leaves the platform and you may neglect the mass of the rope. At the bottom of the circular trajectory, the child and tire are a height h3 = 0.99 m above the ground. include a diagram showing the physical sites (a) Calculate the speed of the child/tire at the bottom of the circular trajectory. m/s (b) Calculate the maximum tension in the rope as the child/tire swing back and forth. N
- An electric motor is used to drive the shaft of a small water pump. During a performance test, the torque on the motor shaft is found to be 7.642 Nm when the motor is drawing 631.33 W of electrical power. What is the rotational speed of the shaft in rpm?LO 6.3 13.) 1 2 (a) (b) 2.5 m Floor [ANS : 2.80 m s¹², 3.51 NJ FIGURE 6.9 FIGURE 6.9 shows a light string wound around a 2 kg pulley is attached to a 5 kg load. The height of the load is 2.5 m above the floor. When the load is released, the pulley starts to rotate and the load descends to the floor. The moment of inertia of the pulley is I = MR². Determine the speed of the load just before it hits the floor. If the string suddenly snaps while the load is 1.5 m above the floor, explain qualitatively why the load would hit the floor with higher speed than that of (a). [ANS: 6.39 m s¹]Starting from rest, a basketball rolls from the top to the bottom of a hill, reaching a translational speed of 6.3 m/s. What is the height of the hill?(Ignore frictional losses) 2.0 m 3.4 m 4.1 m 6.1 m