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A wooden block of mass 50 kg is placed on a smooth horizontal surface. A constant horizontal force of 'X' N is applied on it while it is at rest. The block acquires a velocity of 10 m/s in 2 s. What is the value of X?
100 N
10 N
25 N
250 N
250 N
To determine the force 'X', we calculate the acceleration of the block using kinematic equations and then apply Newton's Second Law of Motion. Given the mass m=50┬аkg, initial velocity u=0, final velocity v=10┬аm/s, and time t=2┬аs, the force is calculated as F=ma=250┬аN.
To determine the force 'X', we calculate the acceleration of the block using kinematic equations and then apply Newton's Second Law of Motion. Given the mass m=50┬аkg, initial velocity u=0, final velocity v=10┬аm/s, and time t=2┬аs, the force is calculated as F=ma=250┬аN.
Pushing a heavy shopping cart in a supermarket: if you push a heavier cart (more mass) and want it to reach a certain speed (velocity) quickly (time), you need to exert a significantly stronger push (force).
v=u+at тАФ First kinematic equation for constant acceleration
F=ma тАФ Newton's second law of motion
The calculation relies on Newton's Second Law of Motion, which states that the force acting on an object is equal to the product of its mass and acceleration (F=ma). First, we find the uniform acceleration using the kinematic formula v=u+at, where a=tvтИТuтАЛ. Substituting the values, we get a=210тИТ0тАЛ=5┬аm/s2. Finally, multiplying mass by this acceleration yields the applied force.
Newton's Second Law defines force as the rate of change of momentum.
Acceleration is the change in velocity per unit time.
A 'smooth' surface implies a coefficient of friction ╬╝=0, meaning no resistive force opposes the motion.
Application of basic Newtonian mechanics to solve dynamic problems.
Assumes ideal conditions (no friction or air resistance).
Calculating engine thrust for accelerating vehicles.
Designing safety systems in automotive engineering.
Standard gravitational acceleration gтЙИ9.8┬аm/s2 is not involved here as motion is horizontal.
Option A (100 N) results from ignoring the time factor; Option B (10 N) is a calculation error; Option C (25 N) implies an incorrect acceleration calculation.
D is correct тАФ Using Newton's Second Law, the product of the mass 50┬аkg and the acceleration 5┬аm/s2 results in a force of 250┬аN.
Always verify units before calculation; ensure mass is in kg, velocity in m/s, and time in seconds to obtain force directly in Newtons.
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