Question

1. A pump lifts 1000 (liters) of water from ground to a tank on the roof of a building 100 (m) high. What is the potential energy in the water? [ 1 (liter) = 1000 cm3 ]. Show all your steps to the solution.

2. A skier is coming downhill. At one point she is 50 (m) above the bottom of the hill and moving at 20 (m/s). What is her speed as she reaches the bottom of the hill?

1. 22.3 (m/s) b. 37.5 (m/s) c. 44.8 (m/s) d. Cannot say without her mass

3. A car of mass 1000 (kg) and moving at 60 (mph) collides with a barrier and comes to a stop in

0.5 (s). Ignoring friction, what is the value of the force that acts on the car?

1. 0 b. 20,000 (N) c. 450, 000 (N) d. 900,000 (N)

4. A coil spring has an elastic constant of 200 (N/m). If it is compressed by 20 (cm), what is the energy stored in the spring?

1. 4 (J) b. 10 (J) c. 20 (J) d. 40 (J)

5. A 60 (kg) sprinter starts from rest and reaches a speed of 12 (m/s) in 6 (s). What is the power that she must have to reach this speed?

1. 720 (J) b. 720 (W) c. 1440 (W) d. 4320 (J)

15. In the gym a weight-lifter lifts a 50 kg barbell straight up a distance of 50 cm in 0.5 s. What is the work done by the weight-lifter?

1. 25 (W) b. 250 (J) c. 250 (W) d. 500 (J)

16.In the above question, what is Power of the weight-lifter?

1. 25 (W) b. 250 (J) c. 250 (W) d. 500 (W)

17.Consider the following situations.

1. A ball moving at a speed “v” is brought to rest

2. The same ball is thrown from rests o that it moves at speed “v”

3. The same ball is moving at speed “v” is brought to rest and reversed in direction to move at speed “v”

In which case does the ball undergo the largest change in momentum?

1. I b. I and ii c. i, ii and iii d. ii and iii e. iii

18. A cart moving at a velocity “v” collides with an identical stationary cart on air track. The two carts stick together after collision. What is their combined velocity after the collision?

1. v b. 0.5 v c. 0 d. – 0.5 v f. Need more information

19. Two cars, one twice the mass of the other, are stationary on a horizontal road. A person pushes each car separately with the same with the same force for 5 (s). One can say that the momentum of the lighter car compared to the momentum of the heavier car after 5 (s) is

1. Smaller b. Larger c. Same

20. A simple pendulum is pulled up in an arc and let go from a stationary position. As it swings back and forth

1. Its kinetic energy (KE) converts to potential energy (PE) b. Its PE converts to KE

c. Its Potential Energy Converts to Elastic Energy (EE) d. Its EE converts to KE   

e. Its EE converts to PE

Answer 1

1) We know density of water is = 1 g /cm³

and given that 1 litre of water = 1000 cm³

so , 1000 litres of water will be = 1000 *1000

= 10⁶ cm³

and density = mass / volume

so mass of 10⁶ cm³ of water = density * volume

=> 1 *10⁶ = 10⁶ grams

= 10³ Kg

which at a height of 100 m stored in a tank

therefore, potential energy stored in that much amount of water = m x g x h

= 10³ x 9.8 x 100

= 980000 J

2) when a skier climbs down with an initial velocity of 20 m/s

then we can apply , equation of motion, V^2-U² = 2*g*S

where S = height from the bottom of the hill.

V and U = final and initial velocity of the skier

so , V^2-U² = 2*g*S

V² - 20² = 2 * 9.8* 50

V² = 980 + 400

= 1380

so , V = (1380) ^0.5

   = 37 .15 m/s

very close to option b) 37.5 m/s

so correct option is b) 37.5 m/s  speed as she reaches the bottom of the hill

4) A coil spring has an elastic constant of 200 (N/m). If it is compressed by 20 (cm),

then energy stored in the spring = 1/2 *k *x²

= 1/2 * 200 * ( 20*10^-2)²

= 1/2 *200 * 0.04

= 4 J

5) A 60 kg sprinter starts from rest and reaches a speed of 12 m/s in 6 s

power required = Force * velocity achieved

= m x a x v

acceleration = V/ t

= (12 -0 ) / ( 6-0)

= 2 m/ s²

so Force = m*a = 60 * 2 => 120 N

therefore,   power required = Force * velocity achieved

= 120 * 12

= 1440 W

6) from the above options it seems that the acceleration due to gravity should be taken as g = 10 m/s²

also, Work done is given as ,W = Force x displacement

=( mass * acceleration due to gravity) * displacement

= (50 * 10 ) * (50 *10^-2)

= 250 J

moreover , although time has been given t = 0.5 s, then also it has no use . unless it has been asked about power, which says rate of doing work, and here its only asked of work done and Power so 250 Watt is not correct.