A coin is projected with speed 6m s-1 (metres per second) along the horizontal surface of a bench. The coefficient of friction between the coin and the surface is 0.7. Modelling the coin as a particle and assuming no air resistance, find the speed of the coin after 0.3 s.
F=ma=-umg
a=-ug
=-0.7×10
-7m/s
V=u+at
V= 6m/s+(-7×0.3)
V=6-2.1
V=3.9m/s
To find the speed of the coin after 0.3 seconds, we can start by analyzing the forces acting on the coin.
The only force acting on the coin in the horizontal direction is the force of friction. The magnitude of the frictional force can be calculated using the equation:
Frictional force = coefficient of friction * normal force
In this case, the normal force is equal to the weight of the coin since it is resting on a horizontal surface. However, since the coin is modeled as a particle, we assume that its weight is acting at a single point and does not contribute to any rotational motion.
Since there is no information given about the mass of the coin, we can't directly calculate the normal force or weight. But we can still find the net horizontal force acting on the coin using the coefficient of friction.
The net force acting on the coin is given by:
Net force = applied force - frictional force
In this case, the applied force is zero because there is no external force acting on the coin in the horizontal direction. Therefore, the net force is equal to the negative of the frictional force:
Net force = - frictional force
Now, we can use Newton's second law to relate the net force to the acceleration of the coin:
Net force = mass * acceleration
Since the coin is modeled as a particle, we can express its acceleration as the rate of change of its velocity:
Acceleration = (change in velocity) / time = (final velocity - initial velocity) / time
Rearranging the equation, we get:
final velocity = initial velocity + (acceleration * time)
Now, substituting the expressions for net force and acceleration, we have:
- frictional force = mass * ((final velocity - initial velocity) / time)
Multiplying both sides by (-1) to solve for the final velocity, we get:
final velocity = - (frictional force * time) / mass + initial velocity
Now, we can substitute the given values into the equation. The coefficient of friction is 0.7, and the initial velocity is 6 m/s. Let's assume the mass of the coin to be 1 kg (since it is not given):
final velocity = - (0.7 * mass * time) / mass + 6
final velocity = - (0.7 * 1 * 0.3) / 1 + 6
final velocity = - 0.21 + 6
final velocity = 5.79 m/s
Therefore, the speed of the coin after 0.3 seconds is approximately 5.79 m/s.