1. 1.
A spring is used to stop a 100kg package which is sliding on an inclined surface as shown. The spring has a constant k=20kN/m & is held by
cables so that it is initially compressed 100mm. knowing that the package has a velocity of 3m/s in the position shown & that the maximum
additional deflection of the spring is 100mm, determine (a) the coefficient of kinetic friction between the package & the surface, (b) the
distance from the spring at which the package comes to a stop.
2.
A car starts from rest at point 1 & moves without friction down the track shown. Determine (a) the radius of curvature at point 2, where the
normal force exerted by the track on the car is 6 times the weight of the car; (b) the minimum value of y such that a 13m radius of curvature at
point 3 would be safe.
3.
A 500g pellet is pushed against the spring (k=1.5kN/m) at A & released from rest. The maximum deflection of the spring is 200mm. Neglecting
friction, determine the maximum radius of the loop for which the pellet will travel around the loop ABCDE & remain at all times in contact
with the loop.
4.
A 500g sphere is attached to an elastic cord of constant k=100N/m, which is undeformed when the sphere is located at the origin O. knowing
that the sphere may slide without friction on the horizontal surface & that in the position shown its velocity vA has a magnitude of 25m/s,
determine (a) the maximum & minimum distances from the sphere to the origin O; (b) the corresponding values of its speed.
5.
A satellite is launched in a direction parallel to the surface of the earth with a velocity of 50,000 km/hr from an altitude of 500 km. determine
(a) the maximum altitude reached by the satellite; (b) the maximum allowable error in the direction of launching if the satellite is to go into
orbit & come no closer than 250 km to the surface of the earth. Radius of the earth is 6370km.
6.
A 15 kg package with a velocity of 3m/s drops from a chute into a 30 kg cart rolling freely along the horizontal with a velocity of 2m/s.
Determine (a) the final velocity of the cart; (b) the impulse exerted by the cart on the package; & (c) the fraction of the initial energy lost in the
impact.
7.
A ball is thrown against a frictionless, inclined wall. Immediately before the ball strikes the wall, its velocity has a magnitude 3m/s & forms an
angle of 30° with the horizontal. Knowing that e=0.8, determine the magnitude & direction of the velocity of the ball as it rebounds from the
wall.
8.
The magnitude & direction of the velocities of 2 frictionless balls before they strike each other are as shown. Assuming e=0.85, determine the
magnitude and direction of the velocity of each ball after the impact if the mass of ball A is half that of ball B.
9.
Ball B is hanging from an inextensible cord BC. An identical ball A is released from rest when it is just touching the cord at a point 1m above
the point where it strikes ball B. Assuming perfectly elastic impact & no friction, determine the velocity of each ball immediately after the
impact.
10. Block A is dropped from a height of 2m onto a 10kg pan of a spring scale. Assuming the impact to be perfectly plastic, determine the maximum
mass of block A if the total allowable deflection of the spring is 300mm. The constant of the spring is k=15kN/m.