Exam Questions - Test 2

Question 1

Q1) A tennis ball of mass 58g has a rough surface.
A cricket ball of mass 160g has a smooth surface.
Assume that the balls have the same diameter.
Both balls are dropped from the roof of a tall building at the same time and fall through the air to the ground.
Sketch, on the axes below, graphs to show the variations with time of the speed of each ball.
label your graph with a T for the tennis ball and a C for the cricket ball.
No calculation required

Answer 1

Q1) Sketch, on the axes below, graphs to show the variations with time of the speed of each ball.
label your graph with a T for the tennis ball and a C for the cricket ball.

Both lines start with the same initial gradient and the T hits terminal velocity while C hits terminal velocity but C has a higher terminal velocity due to a higher mass

Question 2

Q2) An engineer is investigating the tension in a steel cable supporting a uniform wooden plank as shown in Fig. 4.
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The plank is 2.4m long and has a mass of 50kg. It is pivoted at point P to a vertical post. The cable is fixed to the plank at point Q and the vertical post as shown in Fig. 4. The cable is at an angle of 30° to the plank. The plank is in equilibrium and resting in a horizontal position.

(a) Show that the tension T in the cable is about 460N

Answer 2

(a) Show that the tension T in the cable is about 460N
D = len(T) = (2.4 - 0.5)/2 = 0.95m
(d1mg = d2 * F2) = (0.7 * 490.5 = 1.5 * 228.9)
F2/sin(30) = 228.9/sin(30) = 457.8 = 460N

Question 3

Q3) (a) Explain the difference between speed and velocity
When an insect jumps, it achieves a maximum height of 0.18m and travels a horizontal distance of 0.32m as shown in figure 5. Air resistance is negligible

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(b) Show that the initial velocity is approximately 1.9m/s
(c) Show that the insect is in the air for approximately 0.4s
(d) State the position of the insect when it has its minimum speed during the jump. Explain your answer
(e) Show that the minimum speed of the insect during the jump is approximately 0.8m/s
(f) Determine the initial velocity of the insect

Answer 3

(a) Explain the difference between speed and velocity
Velocity is a vector quantity
vector quantities have magnitude and direction
so velocity has magnitude and direction

Speed is a scalar quantity
scalar quantities have magnitude but no direction
so speed only has magnitude, rather than magnitude and direction like velocity

(b) Show that the initial velocity is approximately 1.9m/s

(c) Show that the insect is in the air for approximately 0.4s
2s/u = t
2(2(0.18)/1.86) = 0.385 = 0.4

(d) State the position of the insect when it has its minimum speed during the jump. Explain your answer
The minimum speed is at the height of the jump because all kinetic energy has been transferred into gravitational energy

(e) Show that the minimum speed of the insect during the jump is approximately 0.8m/s
(f) Determine the initial velocity of the insect

Question 4

Q4) Figure 3 shows a sphere that falls through distance h onto horizontal ground. The sphere hits the ground and rebounds
Figure 4 shows the variation with time t of the velocity v of the sphere.

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(a) Calculate h
(b) Calculate the magnitude of the acceleration of the sphere while it is in contact with the ground

Answer 4

(a) Calculate h
h = (5.6 * 0.57) / 2 + (-5.6 * 0.02) / 2
   = 1.596 + -0.056
   = 1.54m
   = 1.60m

(b) Calculate the magnitude of the acceleration of the sphere while it is in contact with the ground

Question 5

Q5) A signal flare is a projectile that launches into the air from a stationary boat to attract attention in an emergency. The signal flare ignites at the top of its trajectory.
Figure 4 shows the trajectory of the signal flare to the point when it ignites

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The signal flare is launched with a vertical component of velocity of 58m/s from a point 5.0m above sea level. Assume that its weight is the only force acting on the signal flare after it has been launched

(a) Calculate the maximum height above sea level reached by the signal flare
(b) Show that the time is taken for the signal flare to reach the maximum height is approximately 6s
(c) The signal flare is launched at an angle of 70° to the horizontal. Calculate the horizontal distance of the signal flare from its launch point when it reaches its maximum height
(d) In practice, the motion of the signal flare is affected by air resistance. State and explain how air resistance will affect the maximum height and horizontal distance from the launch point at which the signal flare ignites

Answer 5

(a) Calculate the maximum height above sea level reached by the signal flare
s = (0+58)/2)t
= 29t

(b) Show that the time is taken for the signal flare to reach the maximum height is approximately 6s
(c) The signal flare is launched at an angle of 70° to the horizontal. Calculate the horizontal distance of the signal flare from its launch point when it reaches its maximum height
(d) In practice, the motion of the signal flare is affected by air resistance. State and explain how air resistance will affect the maximum height and horizontal distance from the launch point at which the signal flare ignites

decreased height and horizontal distanced travelled due to decrease in kinetic energy, kinetic energy decreases because of air resistance decreasing the velocity of the signal flare.