NAME_______________________
(1) Stunt driver Fearless Freida is performing a loop-the-loop in her frictionless coaster car. She
is initially propelled with speed vo towards the loop, then she coasts around the circular track, of
diameter 10.0 m. Freida and her car have total mass 120 kg.
(a) If her initial speed (vo) is 20 m/s, determine the speed at the top of the loop.
(b) Draw free-body diagrams for the coaster car (with driver) at the two positions shown: the top
(A), and halfway up (B). Show forces involved, and all components of the acceleration.
(c) Find the contact force from the track to the car at the top of the loop (position A).
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NAME_______________________
(2) A small sled is being pulled with constant velocity behind a truck, by a string having an angle
θ = 25° with the horizontal. Between the sled and the ground there is a frictional force equal to
450 N, and the sled (with occupant) has mass 130 kg.
(a) Find the tension in the string.
(b) Find the normal force from the ground to the sled.
(c) Find the power provided by the truck to the sled, if the speed is 12 m/s.
(d) Is work done by the gravitational force mg in this situation? Explain why or why not.
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NAME_______________________
(3) In a region of space, the potential energy of an object is given by U = Axy, in terms of its
position coordinates x and y (and independent of z). A is a constant.
(a) Find a general form for the force on the object at an arbitrary position in this region.
(b) Find the magnitude of the force at the position coordinates (1.0 m, 2.0 m, 3.0 m), if A = 12
J/m2.
(4) A toy cart is propelled on an ice rink by a spring. Initially, the cart is stationary, and the
spring has been compressed by 12 cm. The cart is then released, and travels with no friction,
until it hits a rough patch of ice, with coefficient of friction µ = 0.15 between the cart and the ice.
The cart has mass 9.0 kg, and the spring has spring constant k = 330 N/m.
(a) Find the cart velocity after it leaves the spring, but before hitting the rough ice.
(b) Find the frictional force of the cart on the rough ice.
(c) What distance along the rough ice surface does the cart travel before stopping, assuming it
comes to a complete stop on the rough patch?
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NAME_______________________
(5) Three identical masses are pulled on a horizontal surface, with three ropes as shown. Each
mass has m = 35 kg, and the kinetic coefficient of friction is 0.42.
(a) If the three masses move to the right at constant velocity 0.75 m/s, find the tension in the
left-most rope, between the left mass and the middle mass.
(b) Find the tension, TR, in the right-most rope, which pulls externally to the right.
(c) Find the work done by the rope tension TR during a time when the boxes move a distance 6.0
m.
(6) For the situation shown, find the tension in the upper string.
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