Advertisements
Advertisements
Question
Both the springs shown in the following figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?
Advertisements
Solution
Let the block m be displaced towards left by displacement x.
\[\therefore F_1 = -K_1X\] (compressed)
\[ F_2 = -K_2X\] (expanded)
\[ma = F_1 + F_2\]
\[\Rightarrow a = \frac{- x\left( k_1 + k_2 \right)}{m}\]
i.e. \[\left( k_1 + k_2 \right)\frac{x}{m}\] opposite the displacement or towards the mean position.
APPEARS IN
RELATED QUESTIONS
The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s–2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).
When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by
car moving at 40 km/hr is to be stopped by applying brakes in the next 4 m. If the car weighs 2000 kg, what average force must be applied to stop it?
In a TV picture tube, electrons are ejected from the cathode with negligible speed and they attain a velocity of 5 × 106 m/s in travelling one centimetre. Assuming straight-line motion, find the constant force exerted on the electrons. The mass of an electron is 9.1 × 10−31 kg.
Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.
A force \[\vec{F} = \vec{v} \times \vec{A}\] is exerted on a particle in addition to the force of gravity, where \[\vec{v}\] is the velocity of the particle and \[\vec{A}\] is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?
In a simple Atwood machine, two unequal masses m1 and m2 are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the following figure), m1 = 300 g and m2 = 600 g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds; (b) find the tension in the string; (c) find the force exerted by the clamp on the pulley.
A constant force F = m2g/2 is applied on the block of mass m1 as shown in the following figure. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of m1.
State Newton's second law of motion. Under what condition does it take the form F = ma?
The linear momentum of a body of mass m moving with velocity v is :
A body of mass 5 kg is moving with velocity 2 m s-1. Calculate its linear momentum.
The linear momentum of a ball of mass 50 g is 0.5 kg m s-1. Find its velocity.
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate : The magnitude of the force
State the magnitude and direction of the force of gravity acting on the body of mass 5 kg. Take g = 9.8 m s-2.
How long will a stone take to fall to the ground from the top of a building 80 m high
Why is it advantageous to turn before taking a long jump?
State Newton's second law of motion.
A body of mass 400 g is resting on a frictionless table. Find the acceleration of the body when acted upon by a force of 0.02 N.
What do you mean by linear momentum of a body? A force causes an acceleration of 10 ms-2 in a body of mass 1 kg. What acceleration will be caused by the same force in a body of mass 4 kg?
How does moving your hand backward while catching a cricket ball reduce pain?
