Physics homework #03

1. A worker lifts a weight w by pulling down on a

rope with a force

−

→

F . The upper pulley is attached

to the ceiling by a chain, and the lower pulley
is attached to the weight by another chain. In
terms of w, find the tension in each chain and the
magnitude of the force

−

→

F if the weight is lifted

at constant speed. Include the free-body diagram
or diagrams. Assume weightless rope, pulleys and
chains.

2. A train of mass 6.84 × 10

6

kg is moving at a speed of 80 km/h. The brakes, which produce a net

backward force of 1.93 × 10

6

N, are applied for 25.0 seconds. (a) What is the new speed of the train?

(b) How far has the train travelled in this time?

3. Two bodies with masses m

1

and m

2

> m

1

connected by a thread lie on a smooth (frictionless) table.

A force Q is first applied to the larger and then to the smaller of the bodies. Is the tension of the
thread in both cases the same?

m

1

m

1

m

2

m

2

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Q

Q

4. Two blocks connected by a light rope are being dragged by a horizontal force F . Suppose that

F = 50 N, m

1

= 10 kg, m

2

= 20 kg, and friction coefficient between each block and surface is

µ = 0.1. (a) Determine the tension T , and the acceleration of the system. (b) Remove the friction
between m

2

and the surface. (c) Add another mass, m

3

= 30kg.

5. Two blocks with masses m = 2 kg and M = 3 kg are connected by a cord that passes over a

massless and frictionless pulley. The system is released from rest. Find the tension T in the cord
and acceleration of the masses.

6. What is the value of kinetic friction coefficient

between M and the incline, if we know that the
mass m moves down with a constant velocity v

0

?

Values of M, m, α, v

0

and g are known.

α

m

M

7. Two masses, m

1

= 2kg and m

2

= 3kg, attached by a massless rod parallel to the incline on which

both slide, travel down along the plane with m

1

trailing m

2

. The angle of incline is θ = 30

◦

. The

friction coefficient between m

1

and the incline is µ

1

= 0.2 and between m

2

and the incline it is

µ

2

= 0.1. Find (a) the tension in the rod linking m

1

and m

2

, (b) the common acceleration of the

two masses. Would the answer to (a) and (b) be changed if m

2

trails m

1

?

8. The coefficients of kinetic and static friction be-

tween M and the incline are known to be µ

k

and

µ

s

, respectively.

Values of M and g are also

known. Initially the angle α is zero, and then
gradually increases.

(a) At what angle α

0

the

mass M starts to slide down? (b) What is the
acceleration of the mass M , just after it starts to
slide down? (i.e. when the angle is still approxi-
mately α

0

)

α

M

Maciej Wo loszyn

WFiIS AGH

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