APHY111 Exercises: DYNAMICS -1

Useful info: g = 9.8 m/s2

1) Apparent Weight Loss. A 65-kg woman descends in an elevator that briefly accelerates at 0.2g downward when leaving the floor (see figure 1). She stands on a scale that reads in kg. a) During this acceleration, what is her weight and what does the scale read? b) What does the scale read when the elevator descends at a constant speed of 2 m/s?

2) Man in elevator. A man whose mass is 80 kg stands in an elevator. Find the normal force FN of the floor of the elevator on the standing man in the following cases:

a) The elevator is moving upward with an acceleration of 2.45 m/s2

b) The elevator is moving downward with an acceleration of 2.45 m/s2

c) The elevator is moving upward with a deceleration of 2.45 m/s2

d) The elevator is moving downward with a deceleration of 2.45 m/s2

e) The elevator is moving upward with constant speed (u = 4 m/s).

f) The elevator is moving downward with constant speed (u = 4 m/s).

g) During the upward acceleration in a), i) what is the magnitude ΣF of the net force on the passenger and ii) what is the magnitude of the passenger’s acceleration relative to the elevator ? Does ?

3) Boat pulled from the river bank. a) Calculate the net force exerted on the boat in a river by workers A and B as shown in figure 2. b) If the boat starts from rest and moves a distance of 26.65 m for 10 seconds because of the net force (in the direction of shown in figure 2), then what is the boat’s mass?

4) Pulling a box. A box of mass 15 kg is resting in a smooth surface of a horizontal table. A person pulls the box by an attached cord with a force FP = 60 N with a 30o angle, as shown in figure 3. Calculate: a) the acceleration of the box and b) the magnitude of the upward force FN exerted by the table on the box.

5) Pulling two boxes. Two boxes, A and B, are connected by a lightweight cord and are resting on a smooth table. The boxes have masses 12 kg and 10 kg. A horizontal force FP = 40 N is applied to the 10 kg box, as shown in figure 4. Find: a) the acceleration of each box and b) the tension in the cord connecting the boxes.

6) Atwood’s Machine. A system of two objects is suspended over a pulley by a flexible cable (figure 5). The cable’s mass is negligible and the mass of the pulley, as well as any friction, are very small and ignored. If mA = 10 kg and mB = 8 kg, calculate: a) the acceleration of the heavier object and b) the tension force FT in the cable.

7) Pulley in incline. Two objects are connected by a light string that passes over a frictionless pulley, as in figure 6. Draw the free-body diagrams of both objects. If the incline is frictionless and m1 = 2 kg, m2 = 6 kg and θ = 55.0°, find: a) the accelerations of the objects, b) the tension force FT in the string, and c) the speed of each object 2 s after being released.