3. A piece of candy is accelerated at 3.0 m/s 2 in the direction shown by a, over a frictionless horizontal surface. The acceleration is caused by 3

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1 3. A piece of candy is accelerated at 3.0 m/s 2 in the direction shown by a, over a frictionless horizontal surface. The acceleration is caused by 3 forces, 2 of which are shown. F 1 has a magnitude of 10N and F 2 has a magnitude of 20N. What is the third force in unit vector notation and as a magnitude and angle?

2 5. A crate of mass m is placed on a frictionless inclined plane of angle θ. What is the acceleration of the crate after it is released. Comment on the results you get. Suppose that the crate is released from rest, how long does it take the front edge of the crate to reach the bottom (after traveling distance d) and what is its speed just as it gets there?

3 8. A block of mass m = 2kg is released from rest h = 0.5m from the surface of a table, at the top of a θ = 30 o incline. The frictionless incline is fixed on a table of height H = 2m. a. What is the acceleration of the block as it slides down the incline? b. What is the velocity of the block as it leaves the incline? c. How far from the table will the block land? d. How much time has elapsed between the block was released and when it hits the floor? e. Does the mass of the block affect any of the above calculations? f. Redo the above calculations including a frictional force between the block and the incline with a coefficient of kinetic friction of µ k = 0.57.

4 2. A block, B, of mass M=15Kg hangs by a cord from a knot, K, which hangs from a ceiling by means of two other cords. The cords are assumed to be massless. What are the tensions in the three cords. Assume, further, that the gravitational force on the knot is negligible.

5 4. A traffic light weighing 125N hangs from a cable tied to two other cables. What is the tension in the cables? Under what situation does F T1 = F T2?

6 1. A sliding block, S, is connected by a cord that wraps around a frictionless pulley and is connected to a hanging block, H. The cord and pulley are assumed to be massless. In this situation, the hanging block falls and the sliding block accelerates to the right. What are the accelerations of the sliding block and hanging block and the tension in the cord?

7 6. A block of mass m 1 on a rough, horizontal surface is connected to a ball of mass m 2 by a lightweight cord over a lightweight pulley. A force of magnitude F at an angle θ with respect to the horizontal is applied. The coefficient of friction between the block and the surface is µ k. What is the magnitude of the acceleration of the two objects.

8 7. A ball of mass m 1 and a block of mass m 2 are connected by a lightweight cord that passes over a frictionless pulley of negligible mass. The block lies on a wooden surface with a coefficient of friction µ k =0.2. What is the acceleration of the objects and the tension in the cord?

9 9. A fire/rescue helicopter caries a 620kg bucket of water at the end of a 20m long cable. As the aircraft flies back from a fire at constant speed of 40m/s, the cable makes an angle of 40 o with respect to the vertical. a. What is the force due to air resistance on the bucket? b. After filling the bucket with water, the pilot returns to the fire at the same speed with the bucket now making a 7 o angle with the vertical. What is the mass of the water in the bucket?

10 10.If you jump from a desktop and land stiff-legged on a concrete floor, you run a significant risk that you will break a leg. To see how that happens, consider the average force stopping your body when you drop from rest from a height of 1.00 m and stop in a much shorter distance d. Your leg is likely to break at the point where the cross-sectional area of the bone (the tibia) is smallest. This point is just above the ankle, where the cross-sectional area of one bone is about 1.60 cm 2. A bone will fracture when the compressive stress on it exceeds about N/m 2. If you land on both legs, the maximum force that your ankles can safely exert on the rest of your body is then about 2( N/m 2 )( m 2 ) = N Calculate the minimum stopping distance d that will not result in a broken leg if your mass is 60.0 kg. Don t try it! Bend your knees!