1
HW3 - FORCES
1. A boy exerts a 36-N horizontal force as he pulls a 52-N sled across a cement sidewalk at constant speed. What is the coefficient
of kinetic friction between the sidewalk and the metal sled runners? Ignore air resistance.
2.
A force of 40.0 N accelerates a 5.0-kg block at 6.0 m/s2 along a horizontal surface.
a. How large is the frictional force?
b. What is the coefficient of friction?
3.
You pull your 18-kg suitcase at constant speed on a horizontal floor by exerting a 43-N force on the handle, which makes
an angle with the horizontal. The force of friction on the suitcase is 27 N.
a. What angle does the handle make with the horizontal?
b. What is the normal force on the suitcase?
c. What is the coefficient of friction?
4.
Two forces act on a 16-kg object. The first force has a magnitude of 68 N and is directed 24° north of east. The second force
is 32 N, 48° north of west. What is the acceleration of the object resulting from the action of these two forces?
5.
Two forces act on a 4.5-kg block resting on a frictionless surface as shown.
acceleration of the block?
What is the magnitude of the horizontal
2
6.
A 1000-kg elevator is rising and its speed is increasing at 3 m/s2. The tension in the elevator cable is:
7.
A 700-kg elevator accelerates downward at 3.0 m/s2. The tension force of the cable on the elevator is:
8.
A 25magnitude of the normal force of the floor on the chair is:
9.
A 20.0-kg package is dropped from a high tower in still air and is "tracked" by a radar system. When the package is 25 m
above the ground, the radar tracking indicates that its acceleration is 7.0 m/s2. Determine the force of air resistance on the
package.
10.
A 32-N force,
above the horizontal. The mass of the crate is:
3
11.
A 10-kg block is connected to a 40-kg block as shown in the figure.
force of 50 N pulls the blocks to the right.
The surface on which the blocks slide is frictionless.
A
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
12. A 400-N block is dragged along a rough (k = 0.4) horizontal surface by an applied force F as shown. The block moves
at constant velocity. The magnitude of
F is:
13. Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, the
magnitude of the acceleration of each block is:
14.
A 70 N block and an 35-N block are connected by a string as shown. If the pulley is massless and the surface is frictionless, the
magnitude of the acceleration of the 70-N block is:
4
15.
Two blocks weighing 250 N and 350 N respectively, are connected by a string that passes over a massless pulley as shown. The
tension in the string is:
16.
A system of two cables supports a 150-N ball as shown.
a) What is the tension in the right-hand cable?
b) What is the tension in the horizontal cable?
17.
At an art auction, Whitney has acquired a painting that now hangs from a nail on her wall, as shown in the figure. If the painting
has a mass of 12.6 kg, what is the tension in each side of the wire supporting the painting?
18.
A flower pot of mass 4.20 kg is hung above a window by three ropes, each making an angle of 15.000 with the vertical, as
shown. What is the tension in each rope supporting the flower pot?
19.
At a playground, a child slides down a slide that makes a 42° angle with the horizontal direction. The coefficient of kinetic
friction for the child sliding on the slide is 0.20. What is the magnitude of her acceleration during her sliding?
5
20.
A 12-kg crate rests on a horizontal surface and a boy pulls on it with a force that is 300 above the horizontal. If the coefficient of
static friction is 0.40, the minimum magnitude force he needs to start the crate moving is:
21.
A 25-N crate slides down a frictionless incline that is 250 above the horizontal. The magnitude of the normal force of the incline
on the crate is:
22.
/s2)
is:
23.
A block is placed on a rough wooden plane. It is found that when the plane is tilted 300 to the horizontal, the block will slide
down at constant speed. The coefficient of kinetic friction of the block with the plane is:
24.
A rope holds a 10-kg rock at rest on a frictionless inclined plane as shown.
6
a) Determine the tension in the rope.
b)
Which one of the following statements concerning the force exerted on the plane by the rock is true?
A) It is 0 N.
B) It is 98 N.
C) It is greater than 98 N.
D) It is less than 98 N, but greater than zero newtons.
E)
It increases as the angle of inclination is increased.
c) Determine the magnitude of the acceleration of the rock down the inclined plane if the rope breaks?
A) 0 m/s2
B) 4.9 m/s2
C) 5.7 m/s2
D) 8.5 m/s2
E) 9.8 m/s2
25.
Linc, the 65.0- kg lifeguard, slides down a water slide that is inclined at an angle of 35.00 to the horizontal, into the community
swimming pool. if the coefficient of friction of the slide is 0.050, what is Linc’s acceleration as he slides down? The fun takes 2.2
seconds. How long is the slide? what is his speed at the bottom?
26.
A crate is sliding down an incline that is 350 above the horizontal. If the coefficient of kinetic friction is 0.40, the acceleration of
the crate is:
27.
Rose is sledding down an ice-covered hill inclined at an angle of 15° with the horizontal. If Rose and the sled have a combined
mass of 54.0 kg, what is the force pulling them down the hill (neglect friction force)?
28.
**At Sea World, a 900.-kg polar bear slides down a wet slide inclined at an angle of 25.0° to the horizontal. The coefficient of
friction between the bear and the slide is 0.0500. What frictional force impedes the bear’s motion down the slide?
7
HW3 - FORCES
Answer Section
SHORT ANSWER
1.
Fn = mg = 52 N
v is constant, therefore a = 0, so Ffr = k Fn k = Ffr /Fn = 0.69
2. Fnet = ma
Fnet = Fapp - Ffr
Ffr = Fapp - Fnet = Fapp – ma = 1.0 x 10 N
Ffr = k Fn = k mg
k = Ffr /mg
k = 0.20
3.
a. Fh – Ffr = 0
Fh = Ffr = 27 N
cos  = Fh / F = 27 N/43 N  = 510
b. Fn + Fv – Fg = 0
(a = 0) Fn = Fg - Fv = mg – F sin  = 18x9.8 – 43 sin 510
c.k = Ffr /Fn = 27 N/ 140 N
k = 0.19
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Fn = 140 N, upward
4.1 m/s2, 52° north of east
1.8 m/s2
12800 N
4.8 kN, up
310 N
56 N
6.5 kg
a) 1 m/s2
b) 10 N
150 N
0.98 m/s2
3.3 m/s2
290 N
a) 300 N
b) 260 N
The weight of the painting is shared equally by two wires, so each wire must support only half of the weight. However, in this
example the wires do not hang vertically, but instead act at an angle with the painting. Therefore, you must use trigonometry to find
the actual tension in the wire.
W = mg = (12.6 kg)(10.0 m/s2) = 126 N
Therefore, each of the wires equally shares 63 N. Call this value Fy, and use trigonometry to find the angle.
450
cos  = adj/hyp = Fy/F
F = Fy /cos = 63 N/0.71 = 89 N
Therefore, each wire holds the painting with a tension or force of 89 N.
18. W = mg = (4.20 kg)(10.0 m/s2) = 42.0 N
each rope supports 1/3 of this, or 14.0N.
cos  = adj/hyp = 14.0 /T
T = 14.0/cos = 14.0 / cos 15.0° = 14.5 N
19. 5.1 m/s2
20. 44 N
21. 23N
8
22. 490
23. 0.577
24. a) 20 N
b) D
c) B
Fn
Fd
Ffr

25.
W = mg = 650 N
cos = adj/hyp = Fn/mg
Fn = mg cos = 532 N
Fnet = Fd – Ffr
sin = opp/hyp = Fd/mg
Fd = mg sin = 373N
a = Fnet/m = 5.32 m/s2
d = ½ at2 = 12.9 m WOW
v = at = 11.7 m/s
Ffr =  Fn = 27 N
Fnet = 346 N
26. 2.4 m/s2
27.
Before beginning the solution, look at all the forces on the sled.
The resultant of these forces ( mg and Fn) is a component of the gravitational force that goes in the direction of the motion of the
sled, or down the slope. It is labeled Fd.
sin  = Fd /mg
Fd = mg sin  = (54.0 kg)(10.0 m/s2) sin 15° = 140 N
28. Remember, the normal force, Fn, always acts perpendicular to the surface on which the object is moving, so it is equal but opposite
to the mg cos component of the weight.
Fn
Fd
Ffr


mg
mg cos
W = mg = 9000 N
cos = adj/hyp = Fn/mg
Fnet = Fd – Ffr
sin = opp/hyp = Fd/mg
a = Fnet/m = 4.84 m/s2
d = ½ at2
t = 6.43 s
Fn = mg cos = 8160 N
Fd = mg sin = 3804N
v = at = 31.1 m/s
Ffr =  Fn = 408 N
Fnet = 4356 N