PHYSICS I PROBLEMS
KINETICS OF A PARTICLE 1
1. What
force must be exerted on block A of mass M M = 100 kg in order for block B of mass m = 10 kg not to fall fall?? The The coefficient of static friction between blocks A and B is 0.55, and the horizontal surface is frictionless.
F
B A
Sol.: F ≥ 1962 N 2. Two
bodies of mass m mass m 1 = 2 kg and m 2 = 4 kg, respectively, are attached by a string. To measure the maximum tension supported by the string two forces in opposite directions are applied applied to the bodies. These These force forcess chang changee with with time time accord according ing to the express expression ionss ( k = 10 N/s). N/s). Calcul Calculate ate the maximum maximum tension tension T F 1 = kt and F 2 = 2kt, kt, respectively (k supported by the string if it is broken after 30 s. Sol.: 400 N
3. The
coefficient of static friction between mass m1 and the surface surface of the incline inclined d plane plane is 0.1. Calcul Calculate ate the range of possible values for the ratio m2 /m1 for which: a) m a) m 2 goes down, b) m b) m 2 goes up, c) m c) m 2 stays at rest. Sol.: a)
m2 m1
0 .589 b) > 0.
c) 0.413 ≤
m2 m1
m2 m1
0 .413 < 0.
m1 m2
30o
≤ 0.589
4. On
a plane inclined at an angle α angle α with the horizontal, a block of mass m is pulled up at a constant constant velocity velocity by a string. string. The coefficient coefficient of kinetic friction friction between between the surface surface of the plane and the block is µ is µ,, and the string makes an angle β angle β with with the inclined plane. At what angle β is tension of the string string a minim minimum? um? Find Find the valu valuee of the tension tension in β is the tension this case. Sol.: Sol.: β = β = arctan µ,
T min min =
sin α + µ cos α mg 1 + µ2
5. To
unload a bound stack of plywood from a truck, the driver first tilts the bed of the truck and then accelerat accelerates es from rest. rest. Knowing Knowing that the coefficients coefficients of friction between the bottom sheet of plywood and the bed are µs = 0.40 and µk = 0.30, determine ( a ) the smallest acceleration of the truck which will cause the stack of plywood to slide, ( b) the acceleration of the truck which causes corner A of A of the stack to reach the end of the bed in 0.9 s. 309m/s2, b) 4.172m/ 172m/s2 Sol.: a ) 0.309m/
.
.
6. A
package is at rest on a conveyor belt which is initially at rest. The belt is started and moves to the right for 1.3 s with a constant acceleration of 2 m/s2 . The belt then moves with a constant deceleration a2 and comes to a stop after a total displacement of 2.2 m. Knowing that the coefficients of friction between the package and the belt are µs = 0.35 and µk = 0.25, determine (a ) the deceleration a2 of the belt, ( b) the displacement of the package relative to the belt as the belt comes to a stop. Sol.: a ) a 2 = 6.63 m/s2 ←, b) 0.321m →
7. A
light cord of length L has an end fixed at a point O of the ceiling. A small ball of mass m is attached to the other end of the cord and moves as a conical pendulum in a horizontal circle with an angular velocity ω about the vertical axis. Find the tension T in the cord. Note: Use the relation v = rω, where v is the tangential velocity of the ball and r is the radius of the horizontal circle. Sol.: T = mLω 2
8. Determine
the proper bank angle θ for the airplane flying at 600 km/h and making a turn of 3 km radius. Note that the force exerted by the air is normal to the supporting wing surface. Sol.: 43.3o
_
9. A
pilot flies an airplane at a constant speed of 600 km/h in the vertical circle of radius 1000 m. Calculate the force exerted by the seat on the 80-kg pilot at point A and at point B . Sol.: N A = 3007 N,
N B = 1437N
_
10. A
54-kg pilot flies a jet trainer in a half vertical loop of 1200 m radius so that the speed of the trainer decreases at a constant rate. Knowing that the pilot’s apparent weights at points A and C are 1680 N and 350 N, respectively, determine the force exerted on her by the seat of the trainer when the trainer is at point B. Sol.: 1126 N 25.6o
11. The
bar OA rotates about a horizontal axis through O with a constant counterclockwise angular velocity ω = 3 rad/s. As it passes the position θ = 0, a small block of mass m is placed on it at a radial distance r = 45 cm. If the block is observed to slip at θ = 50o , determine the coefficient of static friction µ s between the block and the rod. Sol.: µs = 0.549 .
12. A
curve in a speed track has a radius of 300 m and a rated speed of 190 km/h. Knowing that a racing car starts skidding on the curve when traveling at a speed of 285 km/h, determine (a ) the banking angle θ, (b) the coefficient of static friction between the tires and the track under the prevailing conditions, (c ) the minimum speed at which the same car could negotiate the curve. Definition : The rated speed of a banked highway curve is the
speed at which a car should travel if no lateral friction force is to be exerted on its wheels. Sol.: a ) 43.4o , b) 0.392, c ) 124 km/h
