Newtons Second Law

Q. A body of mass $5\text{kg}$ is raised vertically to a height of $10\text{m}$ by a force $170\text{N}$. The velocity of the body at this height will be

1. $9.8\text{m/s}$
2. $15\text{m/s}$
3. $22\text{m/s}$
4. $37\text{m/s}$

Q.

Find the average force needed to accelerate a car weighing 500 kg from rest to 72 km/h in a distance of 25 m.

Q. A boat floating in fresh water displaces $16,000N$ of water. How many newtons of saltwater would it displace if it floats in saltwater of specific gravity $1.17$?

1. $17,600$
2. $16,000$
3. $14,500$
4. $28,400$

Q. A long plank of mass m is initially at rest on a fictionless surface. A small block with mass initial speed \(u_0\) slides on top of the larger plank. The coefficient of friction between the block plank is \(\mu\). Net work done by friction on system if the top block falls off the plank after sliding on length L is

Q. Find the average force needed to accelerate a car weighing $500kg$ from rest to $72km/h$ in a distance of $25m$.

Q.

A body of mass 0.40 kg moving initially with a constant speed of $10m{s}^{-1}$ to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = -5 s, 25 s, 100 s.

Q. a) A bus leaves a stop and accelerates at a constant rate for 5.0 seconds. During this time the bus travels 25 meters. After this the bus travels at a constant speed for 15 seconds. Then the driver notices a red light 18 meters ahead and applies brakes with acceleration $a_b$. Assume that the bus decelerates at a constant rate and comes to a stop sometime later just at the light.
1. What was the initial acceleration of the bus?
2. What was the velocity of the bus after 5 seconds?
3. Calculate $a_b$ .
4. How long did does the bus brake?
b) Two athletes Usha and Shiney are playing athletic games. Usha is running at a constant velocity towards Shiney who is stationary. When Usha is 12 meters away from Shiney, Shiney starts to accelerate at a constant rate of $1.5m{s}^{-2}$.
1. What is the minimum velocity with which Usha needs to run in order to just catch up with Shiney?
2. How long does Usha take to catch up with Shiney?

Q. The force required to row a boat at constant velocity is proportional to square of its speed. If a speed v km/h requires 4 kW, how much power does a speed of 2v km/h require?

1. $32KW$
2. $8KW$
3. $24KW$
4. $16KW$

Q. Consider a car moving along a straight horizontal road with a speed of $72km/h$. If the coefficient of static friction between the tyres and the road is $0.5$, the shortest distance in which the car can be stopped is:
(Take $g=10m/s^2$)

1. $30m$
2. $40m$
3. $72m$
4. $20m$

Q.

A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of $400\mathrm{m}$ in $20\mathrm{s}$. Find its acceleration. Find the force acting on it if its mass is 7 metric tonnes (Hint: 1 metric tonne $=1000\mathrm{kg}$.)

Q.

A 250 g block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of 40 cm/s. If the friction coefficient between the table and the block is 0.1, how for does the block move before coming to rest?

Q. A body of mass $5\text{kg}$ is raised vertically to a height of $10\text{m}$ by a force $170\text{N}$. The velocity of the body at this height will be

1. $9.8\text{m/s}$
2. $15\text{m/s}$
3. $22\text{m/s}$
4. $37\text{m/s}$

Q. A body of mass $5\text{kg}$ is raised vertically to a height of $10\text{m}$ by a force $170\text{N}$. The velocity of the body at this height will be

1. $9.8\text{m/s}$
2. $15\text{m/s}$
3. $22\text{m/s}$
4. $37\text{m/s}$

Q. A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of radius 30 m. What horizontal force on the scooter is needed to make the turn possible?

Q. Tarzan, who weighs $688N,$ swings from a cliff at the end of a vine $18m$ long (Fig. 8-40). From the top of the cliff to the bottom of the swing, he descends by $3.2m.$ The vine will break if the force on it exceeds $950N.$(a) Does the vine break? (b) If no, what is the greatest force on it during the swing? If yes, at what angle with the vertical does it break ?

Q. Velocity of a bullet changes from $u$ to $v$ after passing through a board of thickness $d$. Force of resistance is directly proportional to the velocity. Time of motion of bullet in the board is given by

1. $\frac{d(u-v)}{uv{\log }_e\frac{u}{v}}$
2. $\frac{dv}{u{\log }_e\frac{u}{v}}$
3. $\frac{d{\log }_e\frac{v}{u}}{v-u}$
4. $\frac{du}{v{\log }_e\frac{u}{v}}$

Q. Explain the rise of liquid in the capillary on the basis of pressure difference.

Q. A given $1700kg$ car goes from $18m/s$ to $0m/s$. If this transition took $9sec$, what was the average power supplied by the force causing this deceleration?
Take the car system to be otherwise isolated (i.e. the decelerating force was the only force acting on the car).

1. $-1700W$
2. $-15300W$
3. $-30600W$
4. $-61200W$
5. Cannot be determined from the information given