Question

Fall I- 2017 Exam2-GeneralPhysics」 00 5 of 6 problems,A 6" problem will count towards extra credit, 1. Conservation of Linear Momentum gure 1. A pendulum of string length 20 cm and bob mass of 1 kg at its end, starts from rest. The pendulum -on with a block of mass 2 kg, initially at rest. The collision is swings down a quarter of a circle and collides head elastic. Neglect the mass of the string. (a) Find the speed of the block just after the collision. (b) What maximum height does the pendulum bob rise to after the collision? 2. Conservation of Energy See Figure 2. A block of mass 1 kg has an initial velocity of 10 m/s as it slides down a smooth, frictionless track which levels out at the bottom. The block falls a height of 15 m. The block then encounters a spring with spring constant 98 N/m. The spring is over a friction-illed region in which the coefficient of kinetic friction is 0.2. (a) What is the speed of the block just before it touches the spring? (b) What is the maximum compression of the spring? 3. Rotational Kinematics and Impulse (a) See Figure 3. A string is wrapped around a frictionless pulley (disc-shaped) of mass M- 1 kg and radius R 6 cm. The pulley is initially at rest, and then a constant force of pull acts to unwind the string. After a time of 2 seconds, the angular velocity is 1,000 rev/min. Find the total length of string unwound in the time of 2 seconds (b) See Figure 4. A baseball of mass 100 grams moves to the right at a speed of 20 m/s, and it is then struck head-on by a bat that moves to the left. The figure shows how the force of impact on the ball changes with time. What is the rebound speed of the ball, that is, the speed of the ball as it leaves the bat? 4. Rotational Dynamics and Torque See Figure 5, A uniform solid sphere of mass 5 kg and radius R 10 cm can rotate about a vertical axis on frictionless bearings. A massless cord passes around the equator of the sphere, over a pulley of mass 2 kg and radius r= 1.0 cm, and is attached to a block of mass 2 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. a) What is the speed of the block when it has fallen 1 m after being released from rest? b) Find the tension on the side of the cord connected to the block.

Answer 1

1) conservation of linear momentum

m1 = 1 kg

m2 = 2 kg

just before the collsion,

the sped of m1, u1 = sqrt(2*g*L)

= sqrt(2*9.8*0.2)

= 1.98 m/s

a) speed of the block just after the collsion,

v2 = 2*m1*u1/(m1+m2)

= 2*1*1.98/(1+2)

= 1.32 m/s

b) velocity of pendulum after the collsion,

v1 = (m1-m2)*u1/(m1+m2)

= (1-2)*1.98/(1+2)

= -0.66 m/s

vertical height raised by the pendulum,

h = v1^2/(2*g)

= 0.66^2/(2*9.8)

= 0.022 m

= 2.2 cm