PHYSICS – problem solving exercises
3. Dynamics: force and motion
Notes: air friction is neglected in all cases, magnitude of free fall acceleration is 10 m/s2
Problem 1:
Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N,
acting due east, and the other is 8.0 N, acting 62° north of west. What is the magnitude of the body’s
acceleration?
Problem 2:
If the 1 kg standard body has an acceleration of 2.00 m/s2
at 20.0° to the positive direction of an x axis,
what are the x and y components of the net force acting on the body?
Problem 3:
A 300 kg sledge accelerates from rest to a speed of 35 m/s in 5 s. What is the magnitude of the force exerted
by its motors?
Problem 4:
After reaching the speed of 35 m/s the sledge from Problem 3 starts to move with the constant velocity on
a frictionless ice. What is the magnitude of the force which must be exerted by its motors now?
Problem 5:
A 1.5 tons helicopter is uniformly accelerated in vertical direction. An upward thrust of its motors is 20 kN.
(a) What is the magnitude and direction of the net force?
(b) What is the magnitude of the helicopter’s acceleration?
Problem 6:
A 1.5 tons helicopter is moving upward with a constant speed of 10 m/s.
(a) What is the magnitude and direction of the net force?
(b) What is an upward thrust of the helicopter’s motors?
Problem 8:
An elevator cab and its load have a combined mass of 1600 kg. Find the tension in the supporting cable
when the cab, originally moving downward at 12 m/s, is brought to rest with constant acceleration in a
distance of 42 m.
Problem 9:
There are two forces on the 2.00 kg box in the overhead view of the attached
figure, but only one is shown. For F1
= 20.0 N, a = 12.0 m/s2
, and θ = 30.0°,
find the second force:
(a) as the x and y components
(b) as the magnitude and angle relative to the positive direction of the x axis.
Problem 7:
A 1.5 tons helicopter is moving horizontally with a constant speed of 10 m/s at a constant height of 500 m.
(a) What is the magnitude and direction of the net force?
(b) What is an upward thrust of the helicopter’s motors?
Problem 11:
An elevator cab that weights 27.8 kN moves upward. What is the tension in the cable if the cab’s speed is
(a) increasing at a rate of 1.22 m/s2
(b) decreasing at a rate of 1.22 m/s2
?
Problem 10:
The mass of the block is 8.5 kg and the angle θ is 30°. Find:
(a) the tension in the cord
(b) the normal force acting on the block
(c) If the cord is cut, find the magnitude of the resulting acceleration of
the block. (Assume no friction)
Problem 12: optional
In a two/dimensional tug-of-war, Alex, Betty, and Charles pull horizontally
on an automobile tire at the angles shown in the overhead view of the
figure. The tire remains stationary in spite of the three pulls. Alex pulls with
force FA
of magnitude 220 N, and Charles pulls with force FC
of magnitude
170 N. Note that the direction of FC
is not given. What is the magnitude of
Betty’s force FB
?
Problem 13: optional
A 40 kg girl and an 8.4 kg sled are on the frictionless ice of a frozen lake, 15 m apart but connected by a
rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope. What are the acceleration
magnitudes of (a) the sled and (b) the girl? (c) How far from the girl’s initial position do they meet?