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Name: _____________________________
Class: _________
QUIZ Forces at angles and inclined plane quiz - HON
1. (4 pts) 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:
Vertical: Fn + F sin 𝜃 = mg
Fn = 120 – 0.5 F
Ffr = 𝜇 Fn = 0.4(120 – 0.5 F)
Ffr = 48 – 0.2F
Horizontal: F cos 𝜃 = Ffr
0.866 F = 48 -0.2 F
F= 45 N
2. (4 pts) A 63 kg water skier is pulled up a 14o incline with a force of 512 N parallel to the ramp.
The
coefficient of kinetic friction between the skier and the ramp is 0.27. Find the magnitude and direction
of the skier’s acceleration.
Perpendicular to the surface:
Fn =mg cos 𝜃 = 611 N
Ffr = 𝜇 Fn = 165 N
Parallel to the incine:
512-(mg sin 𝜃 + Ffr) = ma
195 = 63 a
a = 3 m/s2
direction: up the incline
3. (3 pts) A block slides down a frictionless plane that makes an angle of 300 with the horizontal. The acceleration of the block
is:
Perpendicular to the surface:
Fn =mg cos 𝜃
Parallel to the incine:
mg sin 𝜃 = ma
g sin 𝜃 = a
a = 5 m/s2
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4. (8 pts) Answer the following questions for the two block system shown below. The horizontal surface
is frictionless. M1 = 8 kg, M2 = 3.2 kg, and h = 1.4 m.
(
1. T = 8a
2. 32 – T = 3.2a
a) a = 2.86 m/s2
b) T = 22.9 N
c) x=ut+(a/2)t2
1.4 = 1.43 t2
t = 0.98 s
v = u+at
v = 2.8 m/s
(b) The system is released from rest. Determine the accelerations
of block M1 and block M2.
(c) Determine the tension in the string connecting block M1 to block M2.
(d) Determine the time it takes M2 to hit the floor and the speed it has just before hitting the floor.
5. (1 pt) Two forces, one with a magnitude of 3 N and the other with a magnitude of 5 N, are applied to an object. For which
orientations of the forces shown in the diagrams is the magnitude of the acceleration of the object the least?
ANS: I
6. (1 pt) A crate rests on a horizontal surface and a woman pulls on it with a 10-N force. Rank the situations shown below
according to the magnitude of the normal force exerted by the surface on the crate, least to greatest.
a)
1, 2, 3
ANS: e
b)
2, 1, 3
c)
2, 3, 1
d)
1, 3, 2
e)
3, 2, 1
3
6. (2 pts) A body on a smooth horizontal surface is attached to three spring scales P, Q and R as shown below. The body is in
equilibrium with the scales pulling on it at the angles shown. The magnitudes of the forces are not drawn!!!! Only directions!!!
How do the magnitudes of the force readings FP , FQ , and FR on the scales compare?
A. FP = FQ = FR
B. FR > FP = FQ
ANS: B
C. FR < FP = FQ
D. FP + FQ = FR
7. (3 pts) What would a person who weighs 70 N on Earth weigh on a planet that has the same mass as Earth but
half its radius?
70=G (Mm)/R2
G (Mm)/(R/2)2 = 4 G (Mm)/R2 = 280 N
8. (3 pts)A block of mass M= 20 kg is hung by ropes as shown. The system is in equilibrium. The point O
represents the knot, the junction of the three ropes. Find magnitude of the forces.
F1 = F2 (due to symmetry)
200 = 2 F1 sin 300
F1 = F2 =200 N
F3 = 200 N