Newton's laws, force and inertia, momentum, impulse
- A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s^2) Answer: 1. 21 NS Key idea: impulse equals change in momentum, and the velocity direction reverses at the ground. v_before=√(2gh₁)=√(2×9.8×40... 1
- A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is : Answer: 4. along north-east Force is along the change in velocity, vec F∝ Δvec v=vec v_f-vec v_i . Initially the velocity is southward, -vha... 1
- A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s^2) nearly : Answer: 2. 4.2 kg m/s Key idea: impulse equals change in momentum; the velocity reverses. Speed at the ground v=√(2gh)=√(200)≈14.1 m/s. Rebo... 1
- Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : Answer: 3. g/5 Atwood machine: the heavier mass moves down, and both masses share the same acceleration. a=(m₂-m₁)g/m₁+m₂=(6-4)g/6+4=g/5 Ans... 1
- A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is Answer: 4. a=gtanθ For the block to stay at rest on the smooth wedge accelerating right with a , in the wedge frame use a pseudo force ma on... 1
- Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is c… Answer: 1. g/3 , g Key idea: the spring force cannot change instantly, but the string tension vanishes at once. Before cutting, the spring h... 1
- A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be Answer: 4. mV The wall is smooth, so only the component of velocity perpendicular to the wall changes; the parallel component stays the same... 1