Physics homework #05

1. An electrically charged particle is held at rest at the point x = 0, while a second particle with equal

charge is free to move along the positive x-axis. The potential energy of the system is U (x) = C/x
where C is a positive constant that depends on the magnitude of the charges. Derive an expression
for the x-component of force acting on the movable charged particle, as a function of its position.

2. A puck slides on a level, frictionless air-hockey table. The coordinates of the puck are x and y. It is

acted on by a conservative force described by the potential-energy function U (x, y) =

1
2

k(x

2

+ y

2

).

Derive an expression for the force acting on the puck, and find an expression for the magnitude of
the force as a function of position.

3. A soccer ball has a mass of 0.4 kg. Initially, it is moving to the left at 20 m/s, but then it is kicked

and given a velocity at 45

◦

upward and to the right, with a magnitude of 30 m/s. Find the impulse

of the net force and the average net force, assuming a collision time ∆t = 0.01 s.

4. Two gliders, A having mass 0.5 kg and B having mass 0.3 kg, move toward each other with equal

initial speeds of 2 m/s. (a) After they collide, glider B reverses direction of its motion and moves
away with a final velocity of 2 m/s. What is the final velocity of glider A? How do the changes in
momentum and in velocity compare for the two gliders? (b) After they collide, they stick together.
Find the common final x-velocity v

2x

, and compare the initial and final kinetic energies. (c) They

collide in a perfectly elastic collision. What are the velocities of A and B after the collision?

5. A block having mass M = 1 kg lies on a table (Fig.1). A bullet with the mass m = 10 g and velocity

v = 500 m/s hits the block and gets stuck in it. How far will the block move if the coefficient of
friction between the table and the block is µ = 0.7?

Fig.1

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v

Fig.2

b

v

6. A bullet having mass m

b

= 10 g is speeding toward a block of mass m = 1 kg. The bullet is moving

at speed v

b

= 500 m/s and the block is at rest (Fig.2). The bullet collides with the block, embeds

itself into the block, and knocks the block over the edge. The edge is a height h = 2 m above the
ground. How far from the edge does the block (with the bullet inside) land?

7. The ballistic pendulum is a block of 3 kg mass suspended from a thread 2.5 m long. A bullet with

the mass of 9 g hits the block and gets stuck in it, the result being a deflection of the system by an
angle of 18

◦

. Find the bullet’s speed.

8. James and Ron are standing 20.0 m apart on the slippery surface of a frozen pond. Ron has mass

60.0 kg and James has mass 90.0 kg. Midway between the two men a mug of their favourite beverage
sits on the ice. They pull on the ends of a light rope that is stretched between them. When James
has moved 6.0 m toward the mug, how far and in what direction has Ron moved?

9. The mass of a boat is M = 80 kg, the mass of a boy is m = 36 kg. The boy moves from the stern

to the bows of the boat. What distance does the boat move, if its length is l = 2.8 m? (Neglect the
water resistance.)

10. A 20.0-kg projectile is fired at an angle of 60

◦

above the horizontal with a speed of 80.0 m/s. At

the highest point of its trajectory, the projectile explodes into two fragments with equal mass, one
of which falls vertically with zero initial speed. You can ignore air resistance. (a) How far from the
point of firing does the other fragment strike if terrain is level? (b) How much energy is released
during the explosion?

11. A wheel of radius R is initially at rest and starts to rotate with a constant angular acceleration α

z

.

At what time t are the centripetal (normal) and tangential accelerations of a point on the rim equal?

12. A flywheel with a diameter of 0.6 m is mounted on a horizontal axis and given a constant angular

acceleration of 0.5 rad/s

2

. The flywheel is initially at rest. After it has turned through π rad, find

the velocity and the acceleration vectors for the particle on the rim of the flywheel which, at that
instant, is vertically below the axis.

13. A solid ball of mass M rolls without slipping down the ramp inclined at an angle β to the horizontal.

(a) What are the ball’s acceleration and the magnitude of the friction force on the ball? (b) What
minimum value of the static friction coefficient µ

s

is required to guarantee rolling of the ball without

slipping?

14. A wheel and axle system is presented on the figure below (and we know r, R, and I – the total

moment of inertia of the wheel and axle system). Find the effort force F

e

needed to move mass M

upwards: (a) with a constant speed v, (b) with a constant acceleration a.

15. Two weights (75 N and 125 N) are connected by a very light flexible cord that passes over a 50.0-N

pulley of radius 0.3 m. The pulley is a solid uniform disk and is supported by a hook connected to
the ceiling. What force does the ceiling exert on the hook?

16. A yo-yo is made from two uniform disks , each with mass m = 100 g and radius R = 5 cm, connected

by a light axle of radius b = 2 cm. A light, thin string is wound several times around the axle and
then held stationary while the yo-yo is released from rest, dropping as the string unwinds. Find the
linear acceleration of the yo-yo and the tension in the string.

Maciej Wo loszyn

WFiIS AGH

http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/