Session 2: Dynamics&forces Questions

Remedial Discussion Questions Dynamics and Momentum 1. Why do you fall forwards when a moving bus decelerates to a stop and fall backwards when a bus accelerates from rest? 2. A man is parachuting at constant speed towards the surface of the Earth. (i) State the two forces acting on the man. Are they equal? Why? (ii) State the forces which according to Newton's third Law, makes an action-reaction with each of the forces in (i).

pair

3. A body of mass 2.0 kg is moving on a horizontal surface with a speed of 1.4 ms-1 . A force of 0.20 N is applied to the body for 10s in the same direction as the motion. What is the velocity of the body at the end of 10 s? Ignore friction [ 2.4 ms-1 ] 4. A block of mass m is supported by a cord C from a ceiling, and another cord D is attached to the bottom of the block. Explain this: if you give a jerk to D, it will break; but if you pull on D steadily, C will break C m D

5. Three blocks are connected, as shown, on a horizontal frictionless table and pulled to the right with a force T3 = 65 N. If m1 = 12 kg, m2 = 24 kg and m3 = 31 kg, calculate (a) the acceleration of the system (b) the tensions T1 and T2 [ (a) 0.97 ms-2, (b) 35 N, 12 N ] T1 m1

T2 m2

T3 m3

6. A block of mass m1 moves on a level frictionless surface, connected by a light flexible cord passing over a small frictionless pulley to a second hanging block of mass m2. What is the acceleration of the system, and what is the tension in the cord connecting the two blocks? [ Note: the function of the pulley is just to change the direction of the cord ] m1

m2 7

(a) Explain what is meant by the linear momentum of a body. Obtain a relation between p, the linear momentum of a body of mass m, and EK, its kinetic energy. (b) A bullet is fired from a gun into a block which is suspended by thin threads from fixed points. The bullet remains in the block which swings upwards as shown below

Gun barrel

Explain how you would use this equipment to determine the velocity of the bullet 8. In order to stop a car of mass 1500 kg travelling at 30 ms-1, the driver applies his brakes so that F, the total stopping force, increases steadily to a maximum and then decreases to zero a shown in the figure. Stopping force (a) Calculate each of the following quantities: (i) the change in momentum between t = 0 and t = 10 s (ii) the value of Fmax (iii) the maximum negative acceleration of the car

Fmax

t/s 0

10

20

(b) Draw sketch graphs to show the variation with time of (i) the velocity (ii) the distance travelled (c) Explain why this would seem to a passenger to be a more gentle stop than one in which a constant force was applied throughout Forces 9. An explorer intends to set off on a round-the-trip in a spherical, helium-filled balloon. The balloon has a radius of 12 m. The balloon, support cables and basket have a total mass of 196 kg. What maximum load M can the balloon carry? Take density of helium to be 0.16 kgm-3, and of air to be 1.25 kgm-3 [ 7690 kg ] 10. A wooden cube of mass 100 kg rests on a rough surface as shown below. The length of each side is 0.6 m. The tension of the rope is gradually increased. For what value of the tension will the cube start to have its edge lifted from the floor? Calculate also the force on the block by the ground if the tension is only 100 N. Draw the force on the diagram. [ 380 N, 950 N ] T 20˚

11. A cubical block of wood 10 cm each side floats at the interface between oil and water as shown below, with its lower surface 2 cm below the interface. The density of the oil is 0.6 gcm-3. What is the mass of the block? What is the pressure at the lower surface of the block due to the liquids? Layer of oil = 10 cm [ 680 g]

10 cm

oil water

Practice questions Measurements 1. The volume rate of flow (V/t) of a fluid through a horizontal pipe of length l and radius r is V  pr 4  t 8lη where p is the pressure difference across the pipe and  is the viscosity of the fluid. A student quotes his results for  as 1.137 × 10-3 kgm-1s-1 and estimates the percentage uncertainties in his measurements of V/t, p, l and r as ± 3%, ±2%, ±0.5%, ±5% respectively. Justify his result for η (ie find the uncertainty in η and hence determine if the accuracy of his result is justified) Recommended time to complete question: 5 min Kinematics 1(a) Define velocity and acceleration (b) Use your definitions in (a) to deduce the equations (i) v = u + at (ii) v2 = u2 + 2as Where v is the final velocity, u the initial velocity, a the acceleration, t the time and s the distance travelled. State the conditions necessary for these two equations to be applicable. 2. A ball is thrown from horizontal ground with an initial velocity of 15ms-1 at an angle of 60˚ to the horizontal, as shown below

15 ms-1 60˚

(i) Calculate, for this ball, the initial values of 1. the vertical component of the velocity 2. the horizontal component of the velocity

(ii) Assuming that air resistance can be neglected, use your answers in (i) to determine 1. the maximum height to which the ball rises 2. the time of flight, ie the time interval between the ball being thrown and returning to ground level 3. the horizontal distance between the point from which the ball was thrown and the point where it strikes the ground (iii) (iv)

Use your answers to (ii) to sketch the path of the ball, assuming air resistance is negligible. Label this path N

1. On your sketch in (iii), draw the path of the ball, assuming that air resistance cannot be neglected. Label this path A 2. Suggest an explanation for any differences between the two paths N and A

Recommended time taken to complete both questions: 15 min