Spring 2024: PH 1110 Practice Exam 2
1. You have been asked to design a model ‘hot wheels’ car track that has a vertical loop with a
radius of 20 cm. The mass of the car can be taken to be 20 g.
a) What is the minimum speed the car must have at the highest point without falling off the track?
b) If the actual speed at the highest point is 1.8 m/s, calculate the magnitude of the normal force
there.
c) What is the normal force at the bottom of the track, assuming the same speed as at the top?
Answers: b) 1.4 m/s c) 0.128 N, c) 0.52 N
2. A circular curve of highway is designed for traffic moving at 60 km/hr.
a) If the radius of the curve is 150m, what is the correct angle of banking of the road?
b) If the curve were not banked, what would be the minimum coefficient of friction between tire
and road that would keep traffic from skidding at this speed?
Answers: a) 10.7 degrees b) 0.189
3. a) One of the moons of Jupiter (Europa) orbits Jupiter in an elliptical orbit with an average
radius of 670, 900 km. The period of the orbit is 3.55 days. From this information, calculate the
mass of Jupiter. Express your answer in kilograms. (10 Points)
Answer: Mass of Jupiter = 1.90 x 1027kg
b) You are given that the acceleration of gravity at the surface of Mars is 0.38 of what it is on
Earth, and that the radius of Mars is 3400 km. Use this information to determine the mass of
Mars. (10 Points). You may take the mass of Earth to be 5.98 x 1024 kg, and the Earth radius to
be 6380km.
Answer: Mass of Mars = 6.5 x 1023 kg
4. Three masses are arranged on the vertices of a triangle, as shown in the diagram below. Assume
that the mass on the top is 25 kg, the mass on the lower right is 56 kg, and the mass on the lower left
is 39 kg.
a) By means of arrows, clearly indicate the directions of each of the forces that act on the mass
located at the top vertex of the triangle.
b) Write down in unit vector notation, the force due to each of the two lower masses acting on the
upper mass.
b) Find the net force on the mass located at the top of the triangle shown below, due to the other
two masses. Assume that the mass on the top is 25 kg, the mass on the lower right is 56 kg, and the
mass on the lower left is 39 kg. Give in i, j form.
Assume G = 6.67 x 10-11 Nm2/kg2
Answer: c) (2.66 i + 9.00 j) nN
5. A car is trying to safely navigate a segment of curved highway banked at an angle of 15°. Given
that there is a coefficient of static friction between the car and the road of 0.33, and that the radius
of the curve is 40 m, calculate the maximum velocity for the car to not skid while navigating the
curve. If needed, assume the mass of the car to be 1500 kg.
Answer: 15.56 m/s
6. A 3-kilogram mass moving at 2 m/s is pulled 35 meters up a 25° incline by a force F (see diagram
below).
If the coefficient of friction between the mass and the incline is 0.3, calculate the following:
a.) How much work does gravity do as the mass moves up the incline to the 35-meter mark?
b.) How much work does friction do as the mass moves up the incline to the 35-meter mark?
c.) How much work does the normal force do as the mass moves up the incline to the 35- meter
mark?
d.) How much kinetic energy does the mass initially have?
e.) Assuming the mass's velocity at the 35-meter mark is 7 m/s, use the work/energy theorem to
determine the force F.
Answers: a) -434.87 J b) -279.78 J c) 0 J d) 6 J e) 22.34 N
7. A vertical spring whose spring constant is 900 N/m, is attached to a table and is compressed 0.150
m. Ignore the mass of the spring.
(a) What speed can it give to a 0.300-kg ball when released? (12 Points)
(b) How high above its original position (spring compressed) will the ball fly? (13 Points)
(Hint: Use conservation of energy methods)
Answers: a) 8.035 m/s
b) 3.44 m
8. A spring of spring constant k = 5 x 103 N/m is stretched initially by 5 cm from its unstretched
(equilibrium) position. Calculate the work done to stretch it further by another 5 cm:
a) by computing the area under the graph of F vs x between the appropriate limits
b) by using integration
Answers: a) 18.75 J b) 18.75 J
9. A roller coaster car of mass m = 200 kg is released from rest at the top of a 60-m high hill (position
A), and rolls with negligible friction down the hill, through a circular loop of radius 20 m (positions
B, C, and D, as shown in the diagram below:
a) What is the velocity of the car at position B?
b) What is the velocity of the car at position C?
c) What is the velocity of the car at position D?
d) determine the normal force magnitude and direction) exerted by the track on the car at D.
Answers: a) 34.29 m/s b) 28 m/s c) 19.8 m/s d) 1960 N, downward
10. You are given the two vectors: 𝑨⃑ = 3𝒊 ^− 2𝒋^ and 𝑩⃑ = -4 𝒊^ +2𝒋^ +5𝒌^. Determine:
a) The magnitude of each vector
a) 𝑨⃑. 𝑩⃑, i.e. the dot product of the two vectors
b) The angle between the vectors 𝑨⃑ and 𝑩⃑
Answers: a) A = 3.6, B = m6.7 b) -16
c) 138.4º
11. A 75-kg skier grips a moving rope that is powered by an engine and is pulled at a constant speed
to the top of a 23° hill. The skier is pulled a distance x = 220m along the incline and it takes 2.0 min
to the top of the hill. If the coefficient of kinetic friction between the snow and the skis is µ𝒌 = 0.10,
calculate the horsepower of the engine required if 30 such skiers (maximum) are on the rope at one
time?
Answer: 26 hp