Reference no: EM132191273
Q1
Figure 1: Skater smoothly rounding a turn. Centre of mass makes a path of radius r.
A 51 kg skater smoothly rounds a turn so that the path of her centre of mass has a radius of curvature of 5.7 m. Her speed is 5.4 m.s-1.
A. What is the horizontal component of the force the ice exerts on her skate blades?
B. What is the vertical component of the force the ice exerts on her skate blades?
C. At what angle is she leaning over? Give the angle between the vertical and the axis or her body, assuming she is holding her body straight, while executing the turn.
Q2 You whirl a bucket of water in a vertical circle of radius 95 cm.
Figure 2: Bucket whirled in vertical circle.
A. What's the minimum speed that will keep the rope taught?
Q 3 In a typical front-wheel-drive car, 70% of the car's weight rides on the front wheels.
A. If the coe?icient of friction between tires and road is 0.61, what's the car's maximum acceleration?
Q 4 The reservoir at Northfield Mountain Pumped Storage Project is 204 m above the generators and holds 2.20 × 1010 kg of water. The generators can produce electrical energy at the rate of 1.80 GW.
A. Find the total gravitational energy stored in the reservoir, taking zero potential energy at the generators.
B. Find the length of time the station can generate power at the rate of 1.93 GW, before the reservoir is drained. Give your answer in hours.
Q 5 A 24 kg child sits at one end of a 3.3 m long seesaw. The seesaw has its pivot at the centre.
A. Where should her 61 kg father sit so the center of mass will be at the center of the seesaw?
Q 6 In a railroad switch yard, a 51 tonne (1 tonne=10 3 kg) freight car is sent at 9.8 km.h-1 toward a 37 tonne car that is moving in the same direction at 2.8 km.h-1.
A. What is the speed of the pair after they couple together? Give your answer in km.h-1.
B. What fraction of the initial kinetic energy was lost in the collision? Give the ratio
Q 7 You have your bicycle upside-down for repairs. The front wheel is free to rotate and is perfectly balanced except for the 45 g valve stem.
A. If the valve stem is 28 cm from the rotation axis and is located 35° below the horizontal, what is the resulting torque about the wheel's axis?
Q 8 Three equal masses m are located at the vertices of an equilateral triangle of side L, connected by rods of negligible mass.
A. Find expressions for the rotational inertia of this object about an axis through the center of the triangle and perpendicular to its plane. Express your answer in terms of the variablesm and L.
B. Find expressions for the moment of inertia of this object about an axis that passes through one vertex and the midpoint of the opposite side. Express your answer in terms of the variables m and L.
Q 9 A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a rope that is wound on the wheel and attached to it (see figure). The wheel is released from rest and the block descends 1.5 m in 3.00 s without any slipping of the rope. The tension in the rope during the descent of the block is a constant 20 N.
Figure 3: Wheel with frictionless bearing and block suspended by rope. Block descends.
A. What is the moment of inertia of the wheel?
Q 10 A 170 g baseball is pitched at 45 m.s-1 spinning at 51 rads-1. You can treat the baseball as a uniform solid sphere of radius 4.2 cm.
A. What fraction of its kinetic energy is rotational? Give your answer as Krotational
Q 11 A motor is connected to a solid, cylindrical, uniform drum with a diameter of 1.2 m and a mass of 51 kg. A massless rope is attached to the drum and tied at the other end to a 38 kg weight, so the rope will wind onto the drum as it turns.
A. What torque must the motor apply if the weight is to be lifted with an acceleration of 1.1 m.s-2?