H203 Dynamics - 2. Tutorial Solutions (1718)

H203 Tutorial Solutions- Dynamics Page 1 of 8 Self Attempt Questions 1. (a) The time of contact is prolonged while the change in momentum remains the same. Hence the average force applied on the ball by hand will be reduced . By Newton’s 3rd law, the force on hand by ball will be reduced. (b) Prolonging the time of contact, it allows the force to be applied onto the ball for a longer time thereby increasing the change in momentum of the ball. (c) By Newton’s 1 st law, the o bject should fly forward when bus braked suddenly. The claim is not valid. 2. No. It only means that the net force is zero. For example, there can be two forces of equal magnitude acting on the object in opposite direction. 3. (a) Not possible. The acceleration must be in the same direction as the net force in accordance with Newton’s Second Law. (b) Possible. Example: An object thrown vertically upwards. 4. By Newton’s 2nd law, Net force, F = ma 10 – FD = 0.20 x 2.0 FD = 10 – 0.40 = 9.6 N 5. Initial and final velocities of bullet u = 0 ms-1 and v = 320 ms-1 respectively. Since the force on bullet is assumed constant, the bullet undergoes constant acceleration a where a may be found from kinematics: v2 = u2 + 2as 4 2222 1024.6)82.0(2 0320 2  s uva ms-2 By N2L : force on bullet, F = ma = 5.0x10-3 x 6.24 x 104 = 312 N a = 2.0 ms–2 10 N FD = ?

6. 𝐹𝑓𝑜𝑜𝑡𝑏𝑎𝑙𝑙𝑒𝑟 𝑒𝑥𝑒𝑟𝑡𝑠 𝑜𝑛 𝑏𝑎𝑙𝑙 = 𝑑𝑃𝑏𝑎𝑙𝑙 𝑑𝑡 ≈ 𝑃𝑓 − 𝑃𝑖 ∆𝑡 = 𝑚(𝑣𝑓 − 𝑣𝑖) ∆𝑡 = 0.50(10 − 0) 0.20 = 25 N acting in the direction of the initial motion of the ball. 7. (a) Impulse = change in momentum = m(vf – vi) = (70.0)(5.20 – 0) = 364 Ns (b) 𝐹𝑜𝑛 𝑝𝑎𝑠𝑠𝑒𝑛𝑔𝑒𝑟 = 𝑑𝑃𝑝𝑎𝑠𝑠𝑒𝑛𝑔𝑒𝑟 𝑑𝑡 ≈ ∆𝑃 ∆𝑡 = 364 0.832 = 438 N 8. No. The initial total momentum of the system is not zero. For both objects to be at rest, the final total momentum of the system is zero. This would not be possible as it would violate the Principle of Conservation of Momentum. The assumption is there is no net unbalance external force. 9. Initially the clay has momentum directed towards the wall. When it collides and sticks to the wall, it appears that the momentum is zero. It is tempting to conclude that momentum is not conserved. In reality, the momentum of the clay is transferred to the wall and Earth, causing both to move although the speed is too small to be observable due to the enormous mass of wall and Earth. 10 Linear momentum is not conserved . As the ball rolls down an incline, it experiences resultant force acting on it. The impulse will result in a change in momentum hence the momentum will increase. Linear momentum is only conserved when there is no external resultant force acting on the ball.

Tutorial Discussion Questions 11. (a) FYX: force by Y on X WX: weight by Earth on X RX: normal reaction force