v(r) Question 3 (10) 3.1 A particle P of mass m moves under the gravitational attraction of a mass M fixed at the origin O. Initially P is at a distance a from O when it is projected with speed u directly away from O. Find the velocity v as a function of the distance r of P from O. Before solving the problem first conceptualise it with a sketch. (7) 3.2 Determine the velocity of the P at a distance r = 150 km from O if ,u = 2500 ms ¹ and G = 6.67x10-¹¹ Nm²kg ². a B.M the mass of O is 5.9x10²4 kg, a = 6x105 m (3) y²-yi 2₂-1₁ Lat
v(r) Question 3 (10) 3.1 A particle P of mass m moves under the gravitational attraction of a mass M fixed at the origin O. Initially P is at a distance a from O when it is projected with speed u directly away from O. Find the velocity v as a function of the distance r of P from O. Before solving the problem first conceptualise it with a sketch. (7) 3.2 Determine the velocity of the P at a distance r = 150 km from O if ,u = 2500 ms ¹ and G = 6.67x10-¹¹ Nm²kg ². a B.M the mass of O is 5.9x10²4 kg, a = 6x105 m (3) y²-yi 2₂-1₁ Lat
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Transcribed Image Text:v(r)
Question 3 (10)
3.1 A particle P of mass m moves under the gravitational attraction of a mass M fixed at the origin O. Initially
P is at a distance a from O when it is projected with speed u directly away from O. Find the velocity v as a
function of the distance r of P from O. Before solving the problem first conceptualise it with a sketch. (7)
3.2 Determine the velocity of the P at a distance r = 150 km from O if
,u = 2500 ms ¹ and G = 6.67x10-¹¹ Nm²kg ².
-2
a
B.M
the mass of O is 5.9x10²4
kg, a = 6x105 m
(3)
y²-yi
2₂-1₁
Lat
![PHY222
Time: 2 hours
Question 1 (10)
Given the force vectors F= (2,-1,2) and F₂= (-1,0,-3)
1.1 Write the force vectors F, and F, in component form.
1.2 Find the angle between the vectors, F, and F₂.
1.3 Find a unit vector perpendicular to both F, and F₂.
Term 3 Test
Question 2 (10)
2.1 An object moving along a path position vector as a function of time of is given by
F(t) = 2 cos 3tî+2sin3t) + 1k
Victor the tutor claims that the objects' velocity and acceleration vectors are perpendicular to each other.
Do you agree or disagree with Victor? Support your answer with a calculation.
(5)
2.2 A particle P moves along the x-axis with its displacement at time t given by x(t)= 61²-1³ +1, where
x is measured in metres and t in seconds. Find the times at which P is at rest and find its position at these
times.
(5)
v(r)
V = at seza
Question 3 (10)
3.1 A particle P of mass m moves under the gravitational attraction of a mass M fixed at the origin O. Initially
P is at a distance a from O when it is projected with speed u directly away from O. Find the velocity v as a
function of the distance r of P from O. Before solving the problem first conceptualise it with a sketch. (7)
fivee = ma
3.2 Determine the velocity of the P at a distance r = 150 km from O if the mass of O is 5.9x1024 kg, a = 6x105 m
,u = 2500 ms¹ and G = 6.67x10-¹¹ Nm²kg2.
(3)
=
Question 4 (10)
x
4.1 A 5x106 g mass at position F₁ = (3 m, 0 m) and 250 kg mass at position -(0m, -4m) attracts each
5000 lcg
other.
dv
mat
29 July 2022
Marks: 50
а
4.1.1 Conceptualise the problem and clearly shows in your sketch the forces vectors which the two masses
exerts on it other.
(1)
GmM
4.1.2 Determine the gravitational force the 250 kg mass exerts on the 5x10° g mass. Reminder F=
r²
GM
(2)
(3)
(5)
(4)
4.2 A uniform rod of mass M and length 21 lies along the interval [-1, 1] of the y-axis and a particle of mass m is
situated at the point y = b. Find the gravitational force exerted by the rod on the particle. Before solving
the problem first conceptualise it with a sketch.
+1
2 L
E
b
ac
r.
(5)
dv
de
y²-YI
22-yi
51-1
J-3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04260a20-d9b7-4d40-8318-cc78a4c9fab4%2Fabe71867-7637-4825-9114-d793464aaf47%2F4ows9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PHY222
Time: 2 hours
Question 1 (10)
Given the force vectors F= (2,-1,2) and F₂= (-1,0,-3)
1.1 Write the force vectors F, and F, in component form.
1.2 Find the angle between the vectors, F, and F₂.
1.3 Find a unit vector perpendicular to both F, and F₂.
Term 3 Test
Question 2 (10)
2.1 An object moving along a path position vector as a function of time of is given by
F(t) = 2 cos 3tî+2sin3t) + 1k
Victor the tutor claims that the objects' velocity and acceleration vectors are perpendicular to each other.
Do you agree or disagree with Victor? Support your answer with a calculation.
(5)
2.2 A particle P moves along the x-axis with its displacement at time t given by x(t)= 61²-1³ +1, where
x is measured in metres and t in seconds. Find the times at which P is at rest and find its position at these
times.
(5)
v(r)
V = at seza
Question 3 (10)
3.1 A particle P of mass m moves under the gravitational attraction of a mass M fixed at the origin O. Initially
P is at a distance a from O when it is projected with speed u directly away from O. Find the velocity v as a
function of the distance r of P from O. Before solving the problem first conceptualise it with a sketch. (7)
fivee = ma
3.2 Determine the velocity of the P at a distance r = 150 km from O if the mass of O is 5.9x1024 kg, a = 6x105 m
,u = 2500 ms¹ and G = 6.67x10-¹¹ Nm²kg2.
(3)
=
Question 4 (10)
x
4.1 A 5x106 g mass at position F₁ = (3 m, 0 m) and 250 kg mass at position -(0m, -4m) attracts each
5000 lcg
other.
dv
mat
29 July 2022
Marks: 50
а
4.1.1 Conceptualise the problem and clearly shows in your sketch the forces vectors which the two masses
exerts on it other.
(1)
GmM
4.1.2 Determine the gravitational force the 250 kg mass exerts on the 5x10° g mass. Reminder F=
r²
GM
(2)
(3)
(5)
(4)
4.2 A uniform rod of mass M and length 21 lies along the interval [-1, 1] of the y-axis and a particle of mass m is
situated at the point y = b. Find the gravitational force exerted by the rod on the particle. Before solving
the problem first conceptualise it with a sketch.
+1
2 L
E
b
ac
r.
(5)
dv
de
y²-YI
22-yi
51-1
J-3
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